Tamaas — A high-performance library for periodic rough surface contact

Tamaas (from تماس meaning “contact” in Arabic and Farsi) is a high-performance rough-surface periodic contact code based on boundary and volume integral equations. The clever mathematical formulation of the underlying numerical methods (see e.g. doi:10.1007/s00466-017-1392-5 and arxiv:1811.11558) allows the use of the fast-Fourier Transform, a great help in achieving peak performance: Tamaas is consistently two orders of magnitude faster (and lighter) than traditional FEM! Tamaas is aimed at researchers and practitioners wishing to compute realistic contact solutions for the study of interface phenomena.

You can see Tamaas in action with our interactive tutorials.

Library overview

Tamaas is mainly composed of three components:

• Random surface generation procedures

• Model state objects and operators

• Contact solving procedures

These parts are meant to be independent as well as inter-operable. The first one provides an interface to several stochastic surface generation algorithms described in Random rough surfaces. The second provides an interface to a state object Model (and C++ class tamaas::Model) as well as integral operators based on the state object (see Model and integral operators). Finally, the third part provides contact solving routines that make use of the integral operators for performance (see Solving contact).

Tutorials

The following tutorial notebooks can also be used to learn about Tamaas:

• Elastic Contact (live notebook, notebook viewer)

• Rough Surfaces (live notebook, notebook viewer)

Citations

Tamaas is the fruit of a research effort. To give proper credit to its creators and the scientists behind the methods it implements, you can use the tamaas.utils.publications() function at the end of your python scripts. This function scans global variables and prints the relevant citations for the different capabilities of Tamaas used. Note that it may miss citations if some objects are not explicitly stored in named variables, so please examine the relevant publications in doi:10.21105/joss.02121.

Changelog

The changelog can be consulted here.

Seeking help

You can ask your questions on gitlab using this form. If you do not have an account, you can create one on this page.

Contribution

Contributions to Tamaas are welcome, whether they are code, bug, or documentation related.

Code

Please fork Tamaas and submit your patch as a merge request.

Bug reports

You can also contribute to Tamaas by reporting any bugs you find here if you have an account on gitlab. Please read the FAQ before posting.

Quickstart

Here is a quick introduction to get you started with Tamaas.

Installation from PyPI

If you have a Linux system, or have installed the Windows Subsystem for Linux, you can simply run python3 -m pip install tamaas. This installs the latest stable version of Tamaas from PyPI. You can get the latest cutting-edge build of Tamaas with:

python3 -m pip install \
  --extra-index-url https://gitlab.com/api/v4/projects/19913787/packages/pypi/simple \
  tamaas

Note

To limit the number of statically linked dependencies in the wheel package, the builds that can be installed via PyPI or the GitLab package registery do not include parallelism or architecture specific optimizations. If you want to execute Tamaas in parallel, or want to improve performance, it is highly recommanded that you install with Spack or compile from source with the instructions below.

Installation with Spack

If you have Spack installed (e.g. in an HPC environment), you can install Tamaas with the following:

spack install tamaas

This will install an MPI-enabled version of tamaas with Scipy solvers. The command spack info tamaas shows the build variants. To disable MPI, you should disable MPI in the FFTW variant:

spack install tamaas ^fftw~mpi

The Spack package for Tamaas allows installation from the repository with spack install tamaas@master.

You can also use Spack to create container recipes with spack containerize. Here’s an example spack.yaml for Tamaas which creates an image with OpenMPI and NetCDF so that Tamaas can be executed in parallel within the container with Singularity:

spack:
config:
    build_jobs: 2
specs:
- matrix:
    - [py-mpi4py, py-netcdf4, tamaas@master+solvers]
    - ["^openmpi@4 fabrics=ofi,psm2,ucx schedulers=none"]
concretizer:
    unify: true
container:
    format: singularity
    images:
    os: ubuntu:20.04
    spack: develop
    os_packages:
    final:
        - gfortran

Docker image

We provide Docker images that are automatically built and pused to the Gitlab registry for compatibility reasons (mainly with macOS). To get the latest image simply run:

docker pull registry.gitlab.com/tamaas/tamaas
# to rename for convenience
docker tag registry.gitlab.com/tamaas/tamaas tamaas

Then you can run scripts directly:

docker run -v $PWD:/app -t tamaas python3 /app/your_script.py
# or
docker run tamaas tamaas surface --sizes 16 16 --cutoffs 4 4 8 --hurst 0.8 | docker run -i tamaas tamaas contact 0.1 > results.npy

Warning

The provided Docker image and Dockerfile offer limited customization options and are hard-wired to use OpenMPI. If the use case/goal is to run in HPC environements, containers generated with Spack should be preferred, as they allow greater flexibility in the dependency selection and installed packages.

The Dockerfile at the root of the Tamaas repository can be used to build an image containing Tamaas with a full set of dependencies and customize the build options. Simply run:

docker build -t tamaas .

Tip

The following arguments can be passed to docker to customize the Tamaas build (with the --build-arg flag for docker build):

• BACKEND: parallelism model for loops

• FFTW_THREADS: parallelism model for FFTW3

• USE_MPI: compile an MPI-parallel version of Tamaas

See below for explanations.

Singularity container

A singularity container can be created from the docker image with:

singularity build tamaas.sif docker://registry.gitlab.com/tamaas/tamaas

To run the image with MPI:

mpirun singularity exec --home=$PWD tamaas.sif python3 <your_script>

Installation from source

First make sure the following dependencies are installed for Tamaas:

• a C++ compiler with full C++14 and OpenMP support

• SCons (python build system)

• FFTW3

• thrust (1.9.2+)

• boost (pre-processor)

• python 3+ with numpy

• pybind11 (included as submodule)

• expolit (included as submodule)

Optional dependencies are:

• an MPI implementation

• FFTW3 with MPI/threads/OpenMP (your pick) support

• scipy (for nonlinear solvers)

• uvw, h5py, netCDF4 (for dumpers)

• googletest and pytest (for tests)

• Doxygen and Sphinx (for documentation)

Tip

On a HPC environment, use the following variables to specify where the dependencies are located:

• FFTW_ROOT

• THRUST_ROOT

• BOOST_ROOT

• PYBIND11_ROOT

• GTEST_ROOT

Note

You can use the provided Dockerfile to build an image with the external dependencies installed.

You should first clone the git repository with the submodules that are dependencies to tamaas (pybind11 and googletest):

git clone --recursive https://gitlab.com/tamaas/tamaas.git

The build system uses SCons. In order to compile Tamaas with the default options:

scons

After compiling a first time, you can edit the compilation options in the file build-setup.conf, or alternatively supply the options directly in the command line:

scons option=value [...]

To get a list of all build options and their possible values, you can run scons -h. You can run scons -H to see the SCons-specific options (among them -j n executes the build with n threads and -c cleans the build). Note that the build is aware of the CXX and CXXFLAGS environment variables.

Once compiled, you can install the python module with:

scons install prefix=/your/prefix

The above command automatically calls pip if it is installed. If want to install an editable package for development, the best practice is to run the following in a virtual environment:

scons dev

This is equivalent to running pip install -e build-release/python[all]. You can check that everything is working fine with:

python3 -c 'import tamaas; print(tamaas)'

Important build options

Here are a selected few important compilation options:

build_type

Controls the type of build, which essentially changes the optimisation level (-O0 for debug, -O2 for profiling and -O3 for release) and the amount of debug information. Default type is release. Accepted values are:

• release

• debug

• profiling

CXX

Compiler (uses the environment variable CXX by default).

CXXFLAGS

Compiler flags (uses the environment variable CXXFLAGS by default). Useful to add tuning flags (e.g. -march=native -mtune=native for GCC or -xHOST for Intel), or additional optimisation flags (e.g. -flto for link-time optimization).

backend

Controls the Thrust parallelism backend. Defaults to omp for OpenMP. Accepted values are:

• omp: OpenMP

• cpp: Sequential

• tbb (unsupported): Threading Building Blocks

fftw_threads

Controls the FFTW thread model. Defaults to omp for OpenMP. Accepted values are:

• omp: OpenMP

• threads: PThreads

• none: Sequential

use_mpi

Activates MPI-parallelism (boolean value).

More details on the above options can be found in Performance.

Building the docs

Documentation is built using scons doc. Make sure to have the correct dependencies installed (they are already provided in the Docker image).

Running the contact pipe tools

Once installed, the python package provides a tamaas command, which defines three subcommands that can be used to explore the mechanics of elastic rough contact:

• surface generates randomly rough surfaces (see Random rough surfaces)

• contact solves an elastic contact problem with a surface read from stdin (see Solving contact)

• plot plots the surface tractions and displacements read from stdin

Here’s a sample command line for you to try out:

tamaas surface --cutoffs 2 4 64 --size 512 512 --hurst 0.8 | tamaas contact 1 | tamaas plot

Check out the help of each command (e.g. tamaas surface -h) for a description of the arguments.

Running the tests

You need to activate the build_tests option to compile the tests:

scons build_tests=True

Tests can then be run with the scons test command. Make sure you have pytest installed.

Random rough surfaces

The generation of stochatsticly rough surfaces is controlled in Tamaas by two abstract classes: tamaas::SurfaceGenerator and tamaas::Filter. The former provides access lets the user set the surface sizes and random seed, while the latter encodes the information of the spectrum of the surface. Two surface generation methods are provided:

• tamaas::SurfaceGeneratorFilter implements a Fourier filtering algorithm (see Hu & Tonder),

• tamaas::SurfaceGeneratorRandomPhase implements a random phase filter.

Both of these rely on a tamaas::Filter object to provided the filtering information (usually power spectrum density coefficients). Tamaas provides two such classes and allows for Python subclassing:

• tamaas::Isopowerlaw provides a roll-off powerlaw,

• tamaas::RegularizedPowerlaw provides a powerlaw with a regularized rolloff.

Tamaas also provided routines for surface statistics.

Generating a surface

Let us now see how to generate a surface. Frist create a filter object and set the surface sizes:

import tamaas as tm

# Create spectrum object
spectrum = tm.Isopowerlaw2D()

# Set spectrum parameters
spectrum.q0 = 4
spectrum.q1 = 4
spectrum.q2 = 32
spectrum.hurst = 0.8

The spectrum object can be queried for information, such as the root-mean-square of heights, the various statistical moments, the spectrum bandwidth, etc. Then we create a generator object and build the random surface:

generator = tm.SurfaceGeneratorFilter2D([128, 128])
generator.spectrum = spectrum
generator.random_seed = 0

surface = generator.buildSurface()

Important

The surface object is a numpy.ndarray wrapped around internal memory in the generator object, so a subsequent call to buildSurface may change its content. Note that if generator goes out of scope its memory will not be freed if there is still a live reference to the surface data.

Important

If ran in an MPI context, the constructor of SurfaceGeneratorFilter2D (and others) expects the global shape of the surface. The shape can also be changed with generator.shape = [64, 64].

It is common to normalize a surface after it has been generated so that one can scale the surface to a desired stastistic, e.g. to specify the root-mean-square of slopes:

rms_slopes = 0.25
surface /= iso.rmsSlopes()
surface *= rms_slopes

# Compute root-mean-square of slopes in Fourier domain
print(tm.Statistics2D.computeSpectralRMSSlope(surface))
# Compute root-mean-square of slopes with finite differences
# (introduces discretization error)
print(tm.Statistics2D.computeFDRMSSlope(surface))

Note

The spectrum object gives the expected value of surface statistics, but the corresponding value for a surface realization can differ (particularily if the SurfaceGeneratorFilter2D is used). One could normalize a surface with the actual statistic, but this leads to biased quantities when a representative sample of surfaces is used.

Custom filter

Tamaas provides several classes that can be derived directly with Python classes, and tamaas::Filter is one of them. Since it provides a single pure virtual method computeFilter, it is easy to write a sub-class. Here we implement a class that takes a user-defined auto-correlation function and implements the computeFilter virtual function:

import numpy

class AutocorrelationFilter(tm.Filter2D):
    def __init__(self, autocorrelation):
        tm.Filter2D.__init__(self)
        self.autocorrelation = autocorrelation.copy()

    def computeFilter(self, filter_coefficients):
        shifted_ac = numpy.fft.ifftshift(self.autocorrelation)

        # Fill in the PSD coefficients
        filter_coefficients[...] = numpy.sqrt(np.fft.rfft2(shifted_ac))
        # Normalize
        filter_coefficients[...] *= 1 / numpy.sqrt(self.autocorrelation.size)

Here filter_coefficients is also a numpy.ndarray and is therefore easily manipulated. The creation of the surface then follows the same pattern as previously:

# Create spectrum object
autocorrelation = ...  # set your desired autocorrelation
spectrum = AutocorrelationFilter(autocorrelation)

generator = tm.SurfaceGenerator2D()
generator.shape = autocorrelation.shape
generator.spectrum = spectrum

surface = generator.buildSurface()

The lifetime of the spectrum object is associated to the generator when setSpectrum is called.

Surface Satistics

Tamaas provides the C++ class tamaas::Statistics and its wrapper Statistics2D to compute statistics on surfaces, including:

• power spectrum density

• autocorrelation

• spectrum moments

• root-mean-square of heights \(\sqrt{\langle h^2 \rangle}\)

• root-mean-square of slopes (computed in Fourier domain) \(\sqrt{\langle |\nabla h|^2\rangle}\)

All these quantities are computed in a discretization-independent manner: increasing the number of points in the surface should not drastically change the computed values (for a given spectrum). This allows to refine the discretization as much as possible to approximate a continuum. Note that the autocorrelation and PSD are fft-shifted. Here is a sample code plotting the PSD and autocorrelation:

psd = tm.Statistics2D.computePowerSpectrum(surface)
psd = numpy.fft.fftshift(psd, axes=0) # Shifting only once axis because of R2C transform

import matplotlib.pyplot as plt
from matplotlib.colors import LogNorm

plt.imshow(psd.real, norm=LogNorm())

acf = tm.Statistics2D.computeAutocorrelation(surface)
acf = numpy.fft.fftshift(acf)

plt.figure()
plt.imshow(acf)

plt.show()

See examples/statistics.py for more usage examples of statistics.

Model and integral operators

The class tamaas::Model (and its counterpart Model) is both a central class in Tamaas and one of the simplest. It mostly serves as holder for material properties, fields and integral operators, and apart from a linear elastic behavior does not perform any computation on its own.

Units in Tamaas

All quantities in Tamaas are unitless. To put real units onto them, one can use the following equation, which must have a consistent set of units:

\[\frac{u}{L} = \frac{\pi}{k} \frac{p}{\frac{E}{1-\nu^2}}.\]

It relates the surface displacement \(u\) to the pressure \(p\), with the Young’s modulus \(E\), the Poisson coefficient \(\nu\) and the horizontal physical size of the system \(L\) (i.e. the horizontal period of the system). The wavenumber \(k\) is adimensional. This means that \(L\) is the natural unit for lengths (which can be specified when creating the Model object), and \(E^* := E / (1 - \nu^2)\) is the natural unit for pressures (which can be accessed with model.E_star). All other units (areas, forces, energies, etc.) are derived from these two units.

In general, it is a good idea to work with a unit set that gives numerical values of the same order of magnitude to minimize floating point errors in algebraic operations. While this is not always possible, because in elastic contact we have \(u \sim h_\mathrm{rms}\) and \(p \sim h'_\mathrm{rms} E^*\), which are dependent, one should avoid using meters if expected lengths are nanometers for example.

Model types

tamaas::Model has a concrete subclass tamaas::ModelTemplate which implements the model function for a given tamaas::model_type:

tamaas::basic_2d

Model type used in normal frictionless contact: traction and displacement are 2D fields with only one component.

tamaas::surface_2d

Model type used in frictional contact: traction and displacement are 2D fields with three components.

tamaas::volume_2d

Model type used in elastoplastic contact: tractions are the same as with tamaas::surface_2d but the displacement is a 3D field.

The enumeration values suffixed with _1d are the one dimensional (line contact) counterparts of the above model types. The domain physical dimension and number of components are encoded in the class tamaas::model_type_traits.

Model creation and basic functionality

The instanciation of a Model requires the model type, the physical size of the system, and the number of points in each direction:

physical_size = [1., 1.]
discretization = [512, 512]
model = tm.Model(tm.model_type.basic_2d, physical_size, discretization)

Warning

For models of type volume_*d, the first component of the physical_size and discretization arrays corresponds to the depth dimension (\(z\) in most cases). For example:

tm.Model(tm.model_type.basic_2d, [0.3, 1, 1], [64, 81, 81])

creates a model of depth 0.3 and surface size 1², while the number of points is 64 in depth and 81² on the surface. This is done for data contiguity reasons, as we do discrete Fourier transforms in the horizontal plane.

Note

If ran in an MPI context, the constructor to Model expects the global system sizes and discretization of the model.

Tip

Deep copies of model objects can be done with the copy.deepcopy() function:

import copy

model_copy = copy.deepcopy(model)

Note that it only copies fields, not operators or dumpers.

Model properties

The properties E and nu can be used to set the Young’s modulus and Poisson ratio respectively:

model.E = 1
model.nu = 0.3

Tip

The Greenwood–Tripp equivalence, sometimes called Johnson equivalence, allows one to model a normal, frictionless contact between two homogeneous linear, isotropic, elastic materials with rough surfaces \(h_\alpha\) and \(h_\beta\) as the contact of a rigid-rough surface \(h_\beta - h_\alpha\) and a flat elastic solid with an equivalent contact modulus \(E^*\):

\[\frac{1}{E^*} = \frac{1 - \nu_\alpha^2}{E_\alpha^2} + \frac{1 - \nu_\beta^2}{E_\beta^2} = \frac{1}{E^*_\alpha} + \frac{1}{E^*_\beta}\]

Since a model only defines a single set of elastic properties \((E, \nu)\), one can model contact between two different elastic materials by computing \(E^*\) a priori, and setting \((E, \nu) = (E^*, 0)\). The total displacement \(u\) computed by, for example, a contact solver can then be redistributed in proportion according to:

\[\frac{1}{E^*}u = \frac{1}{E_\alpha^*}u_\alpha + \frac{1}{E_\beta^*}u_\beta\]

Note that is equivalence breaks down with friction, plasticity, heterogeneities, anisotropy, etc.

Fields

Fields can be easlily accessed with the [] operator, similar to Python’s dictionaries:

surface_traction = model['traction']
# surface_traction is a numpy array

To know what fields are available, you can call the list function on a model (list(model)). You can add new fields to a model object with the [] operator:model['new_field'] = new_field, which is convenient for dumping fields that are computed outside of Tamaas.

Note

The fields traction and displacement are always registered in models, and are accessible via model.traction and model.displacement.

A model can also be used to compute stresses from a strain field:

import numpy

strain = numpy.zeros(model.shape + [6])  # Mandel--Voigt notation
stress = numpy.zeros_like(strain)

model.applyElasticity(stress, strain)

Tip

print(model) gives a lot of information about the model: the model type, shape, registered fields, and more!

Manipulating fields

Fields are stored in C-contiguous order. The last dimension of any field is always the vector/tensor components, if the number of components is greater than one. The other dimensions are the space dimensions, in z, x, (y) order for volumetric quantities and x, (y) for boundary quantities.

Tip

To select normal component of the surface displacement of a volume_2d model, one can write:

model.displacement[0, ..., 2]

Symmetric tensors are stored in Mandel–Voigt notation as vectors in the form:

\[\underline \sigma = (\sigma_{11}, \sigma_{22}, \sigma_{33}, \sqrt{2}\sigma_{12}, \sqrt{2}\sigma_{13}, \sqrt{2}\sigma_{23}).\]

Integral operators

Integral operators are a central part of Tamaas: they are carefully designed for performance in periodic system. When a Model object is used with contact solvers or with a residual object (for plasticty), the objects using the model register integral operators with the model, so the user typically does not have to worry about creating integral operators.

Integral operators are accessed through the operators property of a model object. The [] operator gives access to the operators, and list(model.operators) gives the list of registered operators:

# Accessing operator
elasticity = model.operators['hooke']

# Applying operator
elasticity(strain, stress)

# Print all registered operators
print(list(model.operators))

Note

At model creation, these operators are automatically registered:

• hooke: Hooke’s elasticity law

• von_mises: computes Von Mises stresses

• deviatoric: computes the deviatoric part of a stress tensor

• eigenvalues: computes the eigenvalues of a symetric tensor field

Westergaard operators are automatically registered when solveNeumann or solveDirichlet are called.

Model dumpers

The submodule tamaas.dumpers contains a number of classes to save model data into different formats:

UVWDumper

Dumps a model to VTK format. Requires the UVW python package which you can install with pip:

pip install uvw

This dumper is made for visualization with VTK based software like Paraview.

NumpyDumper

Dumps a model to a compressed Numpy file.

H5Dumper

Dumps a model to a compressed HDF5 file. Requires the h5py package. Saves separate files for each dump of a model.

NetCDFDumper

Dumps a model to a compressed NetCDF file. Requires the netCDF4 package. Saves sequential dumps of a model into a single file, with the frame dimension containing the model dumps.

The dumpers are initialzed with a basename and the fields that you wish to write to file (optionally you can set all_fields to True to dump all fields in the model). By default, each write operation creates a new file in a separate directory (e.g. UVWDumper creates a paraview directory). To write to a specific file you can use the dump_to_file method. Here is a usage example:

from tamaas.dumpers import UVWDumper, H5Dumper

# Create dumper
uvw_dumper = UVWDumper('rough_contact_example', 'stress', 'plastic_strain')

# Dump model
uvw_dumper << model

# Or alternatively
model.addDumper(H5Dumper('rough_contact_archive', all_fields=True))
model.addDumper(uvw_dumper)
model.dump()

The last model.dump() call will trigger all dumpers. The resulting files will have the following hierachy:

./paraview/rough_contact_example_0000.vtr
./paraview/rough_contact_example_0001.vtr
./hdf5/rough_contact_archive_0000.h5

Important

Currently, only H5Dumper and NetCDFDumper support parallel output with MPI.

Solving contact

The resolution of contact problems is done with classes that inherit from tamaas::ContactSolver. These usually take as argument a tamaas::Model object, a surface described by a tamaas::Grid or a 2D numpy array, and a tolerance. We will see the specificities of the different solver objects below.

Elastic contact

The most common case is normal elastic contact, and is most efficiently solved with tamaas::PolonskyKeerRey. The advantage of this class is that it combines two algorithms into one. By default, it considers that the contact pressure field is the unknown, and tries to minimize the complementary energy of the system under the constraint that the mean pressure should be equal to the value supplied by the user, for example:

# ...
solver = tm.PolonskyKeerRey(model, surface, 1e-12)
solver.solve(1e-2)

Here the average pressure is 1e-2. The solver can also be instanciated by specifying the the constraint should be on the mean gap instead of mean pressure:

solver = tm.PolonskyKeerRey(model, surface, 1e-12, constraint_type=tm.PolonskyKeerRey.gap)
solver.solve(1e-2)

The contact problem is now solved for a mean gap of 1e-2. Note that the choice of constraint affects the performance of the algorithm.

Non-periodic contact

When the primal type is pressure, it is possible to solve a non-periodic normal contact problem by first registering a non-periodic integral operator (based on the DC-FFT method) then telling the contact solver to use it in its energy functional:

tm.ModelFactory.registerNonPeriodic(model, 'dcfft')
solver.setIntegralOperator('dcfft')
solver.solve(1e-2)

Note however that the solver still shifts the displacement field so that the gap is everywhere positive and zero in the contact zones. This loses the information of the absolute displacement relative to the initial position of the surface. This can be recovered post-solve with:

model.operators['dcfft'](model.traction, model.displacement)

The example nonperiodic.py shows an Hertzian contact example.

Computing solutions for loading sequence

The module tamaas.utils defines a convenience function load_path, which generates solution models for a sequence of loads. This allows lazy evalution and reduces boiler-plate:

from tamaas.utils import load_path

loads = np.linspace(0.01, 0.1, 10)
for model in load_path(solver, loads):
    ...  # do some computation on model, e.g. compute contact clusters

The function load_path accepts the following optional arguments:

verbose

Prints solver output (i.e. iteration, cost function and error)

callback

A function to call after each solve, before the next load step. Useful for dumping model in generator expressions.

Contact with adhesion

The second algorithm hidden in tamaas::PolonskyKeerRey considers the gap to be the unknown. The constaint on the mean value can be chosen as above:

solver = tm.PolonskyKeerRey(model, surface, 1e-12,
                            primal_type=tm.PolonskyKeerRey.gap,
                            constraint_type=tm.PolonskyKeerRey.gap)
solver.solve(1e-2)

The advantage of this formulation is to be able to solve adhesion problems (Rey et al.). This is done by adding a term to the potential energy functional that the solver tries to minimize:

adhesion_params = {
    "rho": 2e-3,
    "surface_energy": 2e-5
}

adhesion = tm.ExponentialAdhesionFunctional(surface)
adhesion.setParameters(adhesion)
solver.addFunctionalterm(adhesion)

solver.solve(1e-2)

Custom classes can be used in place of the example term here. One has to inherit from tamaas::Functional:

import numpy

class AdhesionPython(tm.Functional):
    """
    Functional class that extends a C++ class and implements the virtual
    methods
    """

    def __init__(self, rho, gamma):
        super().__init__(self)
        self.rho = rho
        self.gamma = gamma

    def computeF(self, gap, pressure):
        return -self.gamma * numpy.sum(np.exp(-gap / self.rho))

    def computeGradF(self, gap, gradient):
        gradient += self.gamma * numpy.exp(-gap / self.rho) / self.rho

This example is actually equivalent to tamaas::functional::ExponentialAdhesionFunctional.

Tangential contact

For frictional contact, several solver classes are available. Among them, tamaas::Condat is able to solve a coupled normal/tangential contact problem regardless of the material properties. It however solves an associated version of the Coulomb friction law. In general, the Coulomb friction used in contact makes the problem ill-posed.

Solving a tangential contact problem is not much different from normal contact:

mu = 0.3  # Friction coefficient
solver = tm.Condat(model, surface, 1e-12, mu)
solver.max_iter = 5000         # The default of 1000 may be too little
solver.solve([1e-2, 0, 1e-2])  # 3D components of applied mean pressure

Elasto-plastic contact

For elastic-plastic contact, one needs three different solvers: an elastic contact solver like the ones described above, a non-linear solver and a coupling solver. The non-linear solvers available in Tamaas are implemented in python and inherit from the C++ class tamaas::EPSolver. They make use of the non-linear solvers available in scipy:

DFSANESolver

Implements an interface to scipy.optimize.root() wiht the DFSANE method.

NewtonKrylovSolver

Implements an interface to scipy.optimize.newton_krylov().

These solvers require a residual vector to cancel, the creation of which is handled with tamaas::ModelFactory. Then, an instance of tamaas::EPICSolver is needed to couple the contact and non-linear solvers for the elastic-plastic contact problem:

import tamaas as tm

from tamaas.nonlinear_solvers import DFSANESolver

# Definition of modeled domain
model_type = tm.model_type.volume_2d
discretization = [32, 51, 51]  # Order: [z, x, y]
flat_domain = [1, 1]
system_size = [0.5] + flat_domain

# Setup for plasticity
material = tm.materials.IsotropicHardening(model,
                                           sigma_y=0.1 * model.E,
                                           hardening=0.01 * model.E)
residual = tm.Residual(model, material)
epsolver = DFSANESolver(residual)

# ...

csolver = tm.PolonskyKeerRey(model, surface, 1e-12)

epic = tm.EPICSolver(csolver, epsolver, 1e-7, relaxation=0.3)
epic.solve(1e-3)

# or use an accelerated scheme (which can sometimes not converge)

epic.acceleratedSolve(1e-3)

By default, tamaas::EPICSolver::solve() uses a relaxed fixed point. It can be tricky to make it converge: you need to decrease the relaxation parameter passed as argument of the constructor, but this also hinders the convergence rate. The function tamaas::EPICSolver::acceleratedSolve() does not require the tweaking of a relaxation parameter, so it can be faster if the latter does not have an optimal value. However, it is not guaranteed to converge.

Finally, during the first iterations, the fixed point error will be large compared to the error of the non-linear solver. It can improve performance to have the tolerance of the non-linear solver (which is the most expensive step of the fixed point solve) decrease over the iterations. This can be achieved with the decorator class ToleranceManager:

from tamaas.nonlinear_solvers import ToleranceManager, DFSANESolver

@ToleranceManager(start=1e-2,
                  end=1e-9,
                  rate=1 / 3)
class Solver(DFSANESolver):
    pass

# ...

epsolver = Solver(residual)

# or

epsolver = ToleranceManager(1e-2, 1e-9, 1/3)(DFSANESolver)(residual)

Custom Contact Solvers

The tamaas::ContactSolver class can be derived in Python so that users can interface with Scipy’s scipy.optimize.minimize() function or PETSc’s solvers accessible in the Python interface. See examples/scipy_penalty.py for an example on how to proceed.

Working with MPI

Distributed memory parallelism in Tamaas is implemented with MPI. Due to the bottleneck role of the fast-Fourier transform in Tamaas’ core routines, the data layout of Tamaas is that of FFTW. Tamaas is somewhat affected by limitations of FFTW, and MPI only works on systems with a 2D boundary, i.e. basic_2d, surface_2d and volume_2d model types (which are the most important anyways, since rough contact mechanics can yield different scaling laws in 1D).

MPI support in Tamaas is still experimental, but the following parts are tested:

• Rough surface generation

• Surface statistics computation

• Elastic normal contact

• Elastic-plastic contact (with DFSANECXXSolver)

• Dumping models with H5Dumper and NetCDFDumper.

Tip

One can look at examples/plasticity.py for a full example of an elastic-plastic contact simulation that can run in MPI.

Transparent MPI context

Some parts of Tamaas work transparently with MPI and no additional work or logic is needed.

Warning

MPI_Init() is automatically called when importing the tamaas module in Python. While this works transparently most of the time, in some situations, e.g. in Singularity containers, the program can hang if tamaas is imported first. It is therefore advised to run from mpi4py import MPI before import tamaas to avoid issues.

Creating a model

The following snippet creates a model whose global shape is [16, 2048, 2048]:

import tamaas as tm

model = tm.Model(tm.model_type.volume_2d,
                 [0.1, 1, 1], [16, 2048, 2048])
print(model.shape, model.global_shape)

Running this code with mpirun -np 3 will print the following (not necessarily in this order):

[16, 683, 2048] [16, 2048, 2048]
[16, 682, 2048] [16, 2048, 2048]
[16, 683, 2048] [16, 2048, 2048]

Note that the partitioning occurs on the x dimension of the model (see below for more information on the data layout imposed by FFTW).

Creating a rough surface

Similarly, rough surface generators expect a global shape and return the partionned data:

iso = tm.Isopowerlaw2D()
iso.q0, iso.q1, iso.q2, iso.hurst = 4, 4, 32, .5
gen = tm.SurfaceGeneratorRandomPhase2D([2048, 2048])
gen.spectrum = iso

surface = gen.buildSurface()
print(surface.shape, tm.mpi.global_shape(surface.shape))

With mpirun -np 3 this should print:

(682, 2048) [2048, 2048]
(683, 2048) [2048, 2048]
(683, 2048) [2048, 2048]

Handling partitioning edge cases

Under certain conditions, FFTW may assign to one or more processes a size of zero to the x dimension of the model. If that happens, the surface generator will raise a runtime error, which causes a deadlock because it does not exit the processes with zero data. The correct way to handle this edge case is:

from mpi4py import MPI

try:
    gen = tm.SurfaceGeneratorRandomPhase2D([128, 128])
except RuntimeError as e:
    print(e)
    MPI.COMM_WORLD.Abort(1)

This will correctly kill all processes. Alternatively, os._exit() can be used, but one should avoid sys.exit(), as it kills the process by raising an exception, which still results in a deadlock.

Computing statistics

With a model’s data distributed among independent process, computing global properties, like the true contact area, must be done in a collective fashion. This is transparently handled by the Statistics class, e.g. with:

contact = tm.Statistics2D.contact(model.traction)

This gives the correct contact fraction, whereas something like np.mean(model.traction > 0) will give a different result on each processor.

Nonlinear solvers

The only nonlinear solver (for plastic contact) that works with MPI is DFSANECXXSolver, which is a C++ implementation of DFSANESolver that works in an MPI context.

Note

Scipy and Numpy use optimized BLAS routines for array operations, while Tamaas does not, which results in serial performance of the C++ implementation of the DF-SANE algorithm being lower than the Scipy version.

Dumping models

The only dumpers that properly works in MPI are the H5Dumper and NetCDFDumper. Output is then as simple as:

from tamaas.dumpers import H5Dumper

H5Dumper('output', all_fields=True) << model

This is useful for doing post-processing separately from the main simulation: the post-processing can then be done in serial.

MPI convenience methods

Not every use case can be handled transparently, but although adapting existing scripts to work in an MPI context can require some work, especially if said scripts rely on numpy and scipy for pre- and post-processing (e.g. constructing a parabolic surface for hertzian contact, computing the total contact area), the module mpi provides some convenience functions to make that task easier. The functions mpi.scatter and mpi.gather can be used to scatter/gather 2D data using the partitioning scheme expected from FFTW (see figure below). The functions mpi.rank and mpi.size are used to determine the local process rank and the total number of processes respectively.

If finer control is needed, the function mpi.local_shape gives the 2D shape of the local data if given the global 2D shape (its counterpart mpi.global_shape does the exact opposite), while mpi.local_offset gives the offset of the local data in the global \(x\) dimension. These two functions mirror FFTW’s own data distribution functions.

2D Data distribution scheme from FFTW. N0 and N1 are the number of points in the \(x\) and \(y\) directions respectively. The array local_N0, indexed by the process rank, give the local size of the \(x\) dimension. The local_offset function gives the offset in \(x\) for each process rank.

The mpi module also contains a function sequential whose return value is meant to be used as a context manager. Within the sequential context the default communicator is MPI_COMM_SELF instead of MPI_COMM_WORLD.

For other MPI functionality not covered by Tamaas that may be required, one can use mpi4py, which in conjunction with the methods in mpi should handle just about any use case.

Examples

The directory examples/ in Tamaas’ root repository contains example scripts dedicated to various aspects of Tamaas:

statistics.py

This script generates a rough surface and computes its power spectrum density as well as its autocorrelation function.

rough_contact.py

This script generates a rough surface and solves an adhesion-less elastic contact problem.

adhesion.py

This script solves a rough contact problem with an exponential energy functional for adhesion. It also shows how to derive an energy functional in python.

saturation.py

This script solves a saturated contact problem (i.e. pseudo-plasticity) with a rough surface.

stresses.py

This script solves an equilibrium problem with an eigenstrain distribution and a surface traction distribution and writes the output to a VTK file. It demonstrates how the integral operators that Tamaas uses internally for elastic-plastic contact can be used directly in Python.

plasticity.py

This script solves an elastoplastic Hertz contact problem with three load steps and writes the result to VTK files.

scipy_penalty.py

This script shows how to implement a contact solver in python that uses the contact functionals of Tamaas. Here we use Scipy’s scipy.optimize.minimize() function to solve a contact problem with penalty.

nonperiodic.py

This script shows how to solve a non-periodic problem and compute the true surface interference

Performance

Parallelism

Tamaas implements shared-memory parallelism using thrust. The Thrust backend can be controlled with the following values of the backend build option:

omp

Thrust uses its OpenMP backend (the default). The number of threads is controlled by OpenMP.

cpp

Thurst does not run in threads (i.e. sequential). This is the recommanded option if running multiple MPI tasks.

tbb

Thrust uses its TBB backend. Note that this option is not fully supported by Tamaas.

Tip

When using the OpenMP or TBB backend, the number of threads can be manually controlled by the initialize function. When OpenMP is selected for the backend, the environment variable OMP_NUM_THREADS can also be used to set the number of threads.

FFTW has its own system for thread-level parallelism, which can be controlled via the fftw_threads option:

none

FFTW does not use threads.

threads

FFTW uses POSIX/Win32 threads for parallelism.

omp

FFTW uses OpenMP.

Note

As with the Thrust backend, the number of threads for FFTW can be controlled with initialize.

Finally, the boolean variable use_mpi controls wheter Tamaas is compiled with MPI-parallelism. If yes, Tamaas will be linked against libfftw3_mpi regardless of the thread model.

Important

Users wary of performance should use MPI, as it yields remarkably better scaling properties than the shared memory parallelism models. Care should also be taken when compiling with both OpenMP and MPI support: setting the number of threads to more than one in an MPI context can decrease performance.

Integration algorithm

In its implementation of the volume integral operators necessary for elastic-plastic solutions, Tamaas differenciates two way of computing the intermediate integral along \(z\) in the partial Fourier domain:

• Cutoff integration: because the intermediate integral involves kernels of the form \(\exp(q(x-y))\), it is easy to truncate the integral when \(x\) and \(y\) are far apart, especially for large values of \(q\). This changes the complexity of the intermediate integral from \(O(N_1N_2N_3^2)\) (the naive implementation) to \(O(\sqrt{N_1^2 + N_2^2}N_3^2)\).

• Linear integration: this method relies on a separation of variables \(\exp(q(x-y)) = \exp(qx)\cdot\exp(-qy)\). This allows to break the dependency in \(N_3^2\) of the number of operations, so that the overall complexity of the intermediate integral is \(O(N_1N_2N_3)\).

Details on both algorithms can be found in [1]. Tamaas uses linear integration by default because it is faster in many cases without introducing a truncation error. Unfortunatly, it has a severe drawback when considering systems with a fine surface discretization: due to \(q\) increasing with the number of points on the surface, the separated terms \(\exp(qx)\) and \(\exp(-qy)\) may overflow and underflow respectively. Tamaas will warn if that is the case, and users have two options to remedy the situation:

• Change the integration method by calling setIntegrationMethod with the desired integration_method on the Model object you use in the computation.

• Compile Tamaas with the option real_type='long double'. To make manipulation of numpy arrays easier, a dtype is provided in the tamaas module which can be used to create numpy arrays compatible with Tamaas’ floating point type (e.g. x = np.linspace(0, 1, dtype=tamaas.dtype))

Both these options negatively affect the performance, and it is up to the user to select the optimal solution for their particular use case.

Computational methods & Citations

Tamaas uses specialized numerical methods to efficiently solve elastic and elastoplastic periodic contact problems. Using a boundary integral formulation and a half-space geometry for the former allow (a) the focus of computational power to the contact interface since the bulk response can be represented exactly, (b) the use of the fast-Fourier transform for the computation of convolution integrals. In conjunction with a boundary integral formulation of the bulk state equations, a conjugate gradient approach is used to solve the contact problem.

Note

The above methods are state-of-the-art in the domain of rough surface contact. Below are selected publications detailing the methods used in elastic contact with and without adhesion:

• Boundary integral formulation:

  • Stanley and Kato (J. of Tribology, 1997)

• Conjugate Gradient:

  • Polonsky and Keer (Wear, 1999)

  • Rey, Anciaux and Molinari (Computational Mechanics, 2017)

• Frictional contact:

  • Condat (J. of Optimization Theory and Applications, 2012)

For elastic-plastic contact, Tamaas uses a similar approach by implementing a volume integral formulation of the bulk equilibrium equations. Thanks to kernel expressions that are directly formulated in the Fourier domain, the method reduces the algorithmic complexity, memory requirements and sampling errors compared to traditional volume integral methods (Frérot, Bonnet, Anciaux and Molinari, Computer Methods in Applied Mechanics and Engineering, 2019, arxiv:1811.11558). The figure below shows a comparison of run times for an elasticity problem (only a single solve step) between Tamaas and Akantu, a high-performance FEM code using the direct solver MUMPS.

Comparison of run times between the volume integral implementation (with cutoff integration) of Tamaas and an FEM solve step with a Cholesky factorization performed by Akantu+MUMPS. \(N\) is the total number of points.

Further discussion about the elastic-plastic solver implemented in Tamaas can be found in Frérot, Bonnet, Anciaux and Molinari, (Computer Methods in Applied Mechanics and Engineering, 2019, arxiv:1811.11558).

[1]

L. Frérot, “Bridging scales in wear modeling with volume integral methods for elastic-plastic contact,” École Polytechnique Fédérale de Lausanne, 2020 (Section 2.3.2). doi:10.5075/epfl-thesis-7640.

Frequently Asked Questions

Importing tamaas module gives a circular import error on Windows

(Similar to this issue) Installing with pip install tamaas does not work on Windows, as binary distributions are only built for Linux. To use Tamaas in Windows, use the Windows subsystem for Linux, then use pip to install Tamaas, or use the provided Docker images.

What are the units in Tamaas?

All quantities in Tamaas are unitless. To choose a consistent set of units, see Units in Tamaas.

Do contact solvers solve for a total force or an average pressure?

Solvers consider that the argument to the solve() method is an average apparent pressure (or average gap in some cases), i.e. the total force divided by the total system area (in the reference configuration). This means that doubling the system size and solving for the same argument to the solver increases the total load by a factor 4 (for a 2D surface).

scons dev fails to install Tamaas with externally-managed-environment error

Pip now refuses refuses to install a package outside of virtual environments (see PEP 668), even with the --user flag on. This encourages the use of virtual environments, either with venv or virtualenv, which works nicely with scons dev.

However, if one really needs an editable installation outside of a virtual environment, the PIPFLAGS option can be used to circumvent pip’s protections (not recommended):

scons dev PIPFLAGS="--user --break-system-packages"

Warning

If misused this can break your system’s Python packages. Use virtual environments instead!

API Reference

Python API

Tamaas root module

A high-performance library for periodic rough surface contact

See __author__, __license__, __copyright__ for extra information about Tamaas.

• User documentation: https://tamaas.readthedocs.io

• Bug Tracker: https://gitlab.com/tamaas/tamaas/-/issues

• Source Code: https://gitlab.com/tamaas/tamaas

Tamaas C++ bindings

Compiled component of Tamaas

class tamaas._tamaas.AdhesionFunctional

Bases: Functional

__init__(*args, **kwargs)

computeF(self: tamaas._tamaas.Functional, arg0: GridBaseWrap<T>, arg1: GridBaseWrap<T>) → float

Compute functional value

computeGradF(self: tamaas._tamaas.Functional, arg0: GridBaseWrap<T>, arg1: GridBaseWrap<T>) → None

Compute functional gradient

property parameters

Parameters dictionary

setParameters(self: tamaas._tamaas.AdhesionFunctional, arg0: Dict[str, float]) → None

class tamaas._tamaas.AndersonMixing

Bases: EPICSolver

Fixed-point scheme with fixed memory size and Anderson mixing update to help and accelerate convergence. See doi:10.1006/jcph.1996.0059 for reference.

__init__(self: tamaas._tamaas.AndersonMixing, contact_solver: tamaas._tamaas.ContactSolver, elasto_plastic_solver: tamaas._tamaas.EPSolver, tolerance: float = 1e-10, memory: int = 5) → None

acceleratedSolve(self: tamaas._tamaas.EPICSolver, normal_pressure: float) → float

Solves the EP contact with an accelerated fixed-point scheme. May not converge!

property max_iter

property model

property relaxation

solve(self: tamaas._tamaas.EPICSolver, normal_pressure: float) → float

Solves the EP contact with a relaxed fixed-point scheme. Adjust the relaxation parameter to help convergence.

property tolerance

exception tamaas._tamaas.AssertionError

Bases: AssertionError

__init__(*args, **kwargs)

args

with_traceback()

Exception.with_traceback(tb) – set self.__traceback__ to tb and return self.

class tamaas._tamaas.BEEngine

Bases: pybind11_object

__init__(*args, **kwargs)

getModel(self: tamaas._tamaas.BEEngine) → tamaas::Model

property model

registerDirichlet(self: tamaas._tamaas.BEEngine) → None

registerNeumann(self: tamaas._tamaas.BEEngine) → None

solveDirichlet(self: tamaas._tamaas.BEEngine, arg0: GridBaseWrap<T>, arg1: GridBaseWrap<T>) → None

solveNeumann(self: tamaas._tamaas.BEEngine, arg0: GridBaseWrap<T>, arg1: GridBaseWrap<T>) → None

class tamaas._tamaas.BeckTeboulle

Bases: ContactSolver

__init__(self: tamaas._tamaas.BeckTeboulle, model: tamaas._tamaas.Model, surface: GridBaseWrap<T>, tolerance: float, mu: float) → None

addFunctionalTerm(self: tamaas._tamaas.ContactSolver, arg0: tamaas._tamaas.Functional) → None

Add a term to the contact functional to minimize

computeCost(self: tamaas._tamaas.BeckTeboulle, arg0: bool) → float

property dump_freq

Frequency of displaying solver info

property functional

property max_iter

Maximum number of iterations

property model

setDumpFrequency(self: tamaas._tamaas.ContactSolver, dump_freq: int) → None

setMaxIterations(self: tamaas._tamaas.ContactSolver, max_iter: int) → None

solve(self: tamaas._tamaas.BeckTeboulle, p0: List[float]) → float

property surface

property tolerance

Solver tolerance

class tamaas._tamaas.Cluster1D

Bases: pybind11_object

__init__(self: tamaas._tamaas.Cluster1D) → None

property area

Area of cluster

property bounding_box

Compute the bounding box of a cluster

property extent

Compute the extents of a cluster

getArea(self: tamaas._tamaas.Cluster1D) → int

getPerimeter(self: tamaas._tamaas.Cluster1D) → int

getPoints(self: tamaas._tamaas.Cluster1D) → List[List[int[1]]]

property perimeter

Get perimeter of cluster

property points

Get list of points of cluster

class tamaas._tamaas.Cluster2D

Bases: pybind11_object

__init__(self: tamaas._tamaas.Cluster2D) → None

property area

Area of cluster

property bounding_box

Compute the bounding box of a cluster

property extent

Compute the extents of a cluster

getArea(self: tamaas._tamaas.Cluster2D) → int

getPerimeter(self: tamaas._tamaas.Cluster2D) → int

getPoints(self: tamaas._tamaas.Cluster2D) → List[List[int[2]]]

property perimeter

Get perimeter of cluster

property points

Get list of points of cluster

class tamaas._tamaas.Cluster3D

Bases: pybind11_object

__init__(self: tamaas._tamaas.Cluster3D) → None

property area

Area of cluster

property bounding_box

Compute the bounding box of a cluster

property extent

Compute the extents of a cluster

getArea(self: tamaas._tamaas.Cluster3D) → int

getPerimeter(self: tamaas._tamaas.Cluster3D) → int

getPoints(self: tamaas._tamaas.Cluster3D) → List[List[int[3]]]

property perimeter

Get perimeter of cluster

property points

Get list of points of cluster

class tamaas._tamaas.Condat

Bases: ContactSolver

Main solver for frictional contact problems. It has no restraint on the material properties or friction coefficient values, but solves an associated version of the Coulomb friction law, which differs from the traditional Coulomb friction in that the normal and tangential slip components are coupled.

__init__(self: tamaas._tamaas.Condat, model: tamaas._tamaas.Model, surface: GridBaseWrap<T>, tolerance: float, mu: float) → None

addFunctionalTerm(self: tamaas._tamaas.ContactSolver, arg0: tamaas._tamaas.Functional) → None

Add a term to the contact functional to minimize

computeCost(self: tamaas._tamaas.Condat, arg0: bool) → float

property dump_freq

Frequency of displaying solver info

property functional

property max_iter

Maximum number of iterations

property model

setDumpFrequency(self: tamaas._tamaas.ContactSolver, dump_freq: int) → None

setMaxIterations(self: tamaas._tamaas.ContactSolver, max_iter: int) → None

solve(self: tamaas._tamaas.Condat, p0: List[float], grad_step: float = 0.9) → None

property surface

property tolerance

Solver tolerance

class tamaas._tamaas.ContactSolver

Bases: pybind11_object

__init__(self: tamaas._tamaas.ContactSolver, arg0: tamaas._tamaas.Model, arg1: GridBaseWrap<T>, arg2: float) → None

addFunctionalTerm(self: tamaas._tamaas.ContactSolver, arg0: tamaas._tamaas.Functional) → None

Add a term to the contact functional to minimize

property dump_freq

Frequency of displaying solver info

property functional

property max_iter

Maximum number of iterations

property model

setDumpFrequency(self: tamaas._tamaas.ContactSolver, dump_freq: int) → None

setMaxIterations(self: tamaas._tamaas.ContactSolver, max_iter: int) → None

solve(*args, **kwargs)

Overloaded function.

1. solve(self: tamaas._tamaas.ContactSolver, target_force: List[float]) -> float

Solve the contact for a mean traction/gap vector

2. solve(self: tamaas._tamaas.ContactSolver, target_normal_pressure: float) -> float

Solve the contact for a mean normal pressure/gap

property surface

property tolerance

Solver tolerance

class tamaas._tamaas.EPICSolver

Bases: pybind11_object

Main solver class for elastic-plastic contact problems

__init__(self: tamaas._tamaas.EPICSolver, contact_solver: tamaas._tamaas.ContactSolver, elasto_plastic_solver: tamaas._tamaas.EPSolver, tolerance: float = 1e-10, relaxation: float = 0.3) → None

acceleratedSolve(self: tamaas._tamaas.EPICSolver, normal_pressure: float) → float

Solves the EP contact with an accelerated fixed-point scheme. May not converge!

property max_iter

property model

property relaxation

solve(self: tamaas._tamaas.EPICSolver, normal_pressure: float) → float

Solves the EP contact with a relaxed fixed-point scheme. Adjust the relaxation parameter to help convergence.

property tolerance

class tamaas._tamaas.EPSolver

Bases: pybind11_object

Mother class for nonlinear plasticity solvers

__init__(self: tamaas._tamaas.EPSolver, residual: tamaas._tamaas.Residual) → None

beforeSolve(self: tamaas._tamaas.EPSolver) → None

getResidual(self: tamaas._tamaas.EPSolver) → tamaas._tamaas.Residual

getStrainIncrement(self: tamaas._tamaas.EPSolver) → GridBaseWrap<T>

setToleranceManager(self: tamaas._tamaas.EPSolver, arg0: tamaas._tamaas._tolerance_manager) → None

solve(self: tamaas._tamaas.EPSolver) → None

property tolerance

updateState(self: tamaas._tamaas.EPSolver) → None

class tamaas._tamaas.ElasticFunctionalGap

Bases: Functional

__init__(self: tamaas._tamaas.ElasticFunctionalGap, arg0: tamaas::IntegralOperator, arg1: GridBaseWrap<T>) → None

computeF(self: tamaas._tamaas.Functional, arg0: GridBaseWrap<T>, arg1: GridBaseWrap<T>) → float

Compute functional value

computeGradF(self: tamaas._tamaas.Functional, arg0: GridBaseWrap<T>, arg1: GridBaseWrap<T>) → None

Compute functional gradient

class tamaas._tamaas.ElasticFunctionalPressure

Bases: Functional

__init__(self: tamaas._tamaas.ElasticFunctionalPressure, arg0: tamaas::IntegralOperator, arg1: GridBaseWrap<T>) → None

computeF(self: tamaas._tamaas.Functional, arg0: GridBaseWrap<T>, arg1: GridBaseWrap<T>) → float

Compute functional value

computeGradF(self: tamaas._tamaas.Functional, arg0: GridBaseWrap<T>, arg1: GridBaseWrap<T>) → None

Compute functional gradient

class tamaas._tamaas.ExponentialAdhesionFunctional

Bases: AdhesionFunctional

Potential of the form F = -γ·exp(-g/ρ)

__init__(self: tamaas._tamaas.ExponentialAdhesionFunctional, surface: GridBaseWrap<T>) → None

computeF(self: tamaas._tamaas.Functional, arg0: GridBaseWrap<T>, arg1: GridBaseWrap<T>) → float

Compute functional value

computeGradF(self: tamaas._tamaas.Functional, arg0: GridBaseWrap<T>, arg1: GridBaseWrap<T>) → None

Compute functional gradient

property parameters

Parameters dictionary

setParameters(self: tamaas._tamaas.AdhesionFunctional, arg0: Dict[str, float]) → None

class tamaas._tamaas.FieldContainer

Bases: pybind11_object

__init__(self: tamaas._tamaas.FieldContainer) → None

getField(self: tamaas::Model, field_name: str) → GridVariant

getFields(self: tamaas::Model) → List[str]

Return fields list

registerField(self: tamaas::Model, field_name: str, field: numpy.ndarray[numpy.float64]) → None

class tamaas._tamaas.Filter1D

Bases: pybind11_object

Mother class for Fourier filter objects

__init__(self: tamaas._tamaas.Filter1D) → None

computeFilter(self: tamaas._tamaas.Filter1D, arg0: GridWrap<T, dim>) → None

Compute the Fourier coefficient of the surface

class tamaas._tamaas.Filter2D

Bases: pybind11_object

Mother class for Fourier filter objects

__init__(self: tamaas._tamaas.Filter2D) → None

computeFilter(self: tamaas._tamaas.Filter2D, arg0: GridWrap<T, dim>) → None

Compute the Fourier coefficient of the surface

exception tamaas._tamaas.FloatingPointError

Bases: FloatingPointError

__init__(*args, **kwargs)

args

with_traceback()

Exception.with_traceback(tb) – set self.__traceback__ to tb and return self.

class tamaas._tamaas.FloodFill

Bases: pybind11_object

__init__(*args, **kwargs)

static getClusters(contact: GridWrap<T, dim>, diagonal: bool) → List[tamaas._tamaas.Cluster2D]

Return a list of clusters from boolean map

static getSegments(contact: GridWrap<T, dim>) → List[tamaas._tamaas.Cluster1D]

Return a list of segments from boolean map

static getVolumes(map: GridWrap<T, dim>, diagonal: bool) → List[tamaas._tamaas.Cluster3D]

Return a list of volume clusters

class tamaas._tamaas.Functional

Bases: pybind11_object

__init__(self: tamaas._tamaas.Functional) → None

computeF(self: tamaas._tamaas.Functional, arg0: GridBaseWrap<T>, arg1: GridBaseWrap<T>) → float

Compute functional value

computeGradF(self: tamaas._tamaas.Functional, arg0: GridBaseWrap<T>, arg1: GridBaseWrap<T>) → None

Compute functional gradient

class tamaas._tamaas.IntegralOperator

Bases: pybind11_object

__init__(self: tamaas._tamaas.IntegralOperator, arg0: tamaas._tamaas.Model) → None

apply(self: tamaas._tamaas.IntegralOperator, arg0: numpy.ndarray[numpy.float64], arg1: numpy.ndarray[numpy.float64]) → None

dirac = <kind.dirac: 2>

dirichlet = <kind.dirichlet: 1>

getKind(self: tamaas._tamaas.IntegralOperator) → tamaas._tamaas.IntegralOperator.kind

getModel(self: tamaas._tamaas.IntegralOperator) → tamaas._tamaas.Model

getType(self: tamaas._tamaas.IntegralOperator) → tamaas._tamaas.model_type

property kind

matvec(self: tamaas._tamaas.IntegralOperator, arg0: numpy.ndarray[numpy.float64]) → GridBaseWrap<T>

property model

neumann = <kind.neumann: 0>

property shape

property type

updateFromModel(self: tamaas._tamaas.IntegralOperator) → None

Resets internal persistent variables from the model

class tamaas._tamaas.Isopowerlaw1D

Bases: Filter1D

Isotropic powerlaw spectrum with a rolloff plateau

__init__(self: tamaas._tamaas.Isopowerlaw1D) → None

alpha(self: tamaas._tamaas.Isopowerlaw1D) → float

Nayak’s bandwidth parameter

computeFilter(self: tamaas._tamaas.Filter1D, arg0: GridWrap<T, dim>) → None

Compute the Fourier coefficient of the surface

elasticEnergy(self: tamaas._tamaas.Isopowerlaw1D) → float

Computes full contact energy (adimensional)

property hurst

Hurst exponent

moments(self: tamaas._tamaas.Isopowerlaw1D) → List[float]

Theoretical first 3 moments of spectrum

property q0

Long wavelength cutoff

property q1

Rolloff wavelength

property q2

Short wavelength cutoff

radialPSDMoment(self: tamaas._tamaas.Isopowerlaw1D, arg0: float) → float

Computes ∫ k^q ɸ(k) k dk from 0 to ∞

rmsHeights(self: tamaas._tamaas.Isopowerlaw1D) → float

Theoretical RMS of heights

rmsSlopes(self: tamaas._tamaas.Isopowerlaw1D) → float

Theoretical RMS of slopes

class tamaas._tamaas.Isopowerlaw2D

Bases: Filter2D

Isotropic powerlaw spectrum with a rolloff plateau

__init__(self: tamaas._tamaas.Isopowerlaw2D) → None

alpha(self: tamaas._tamaas.Isopowerlaw2D) → float

Nayak’s bandwidth parameter

computeFilter(self: tamaas._tamaas.Filter2D, arg0: GridWrap<T, dim>) → None

Compute the Fourier coefficient of the surface

elasticEnergy(self: tamaas._tamaas.Isopowerlaw2D) → float

Computes full contact energy (adimensional)

property hurst

Hurst exponent

moments(self: tamaas._tamaas.Isopowerlaw2D) → List[float]

Theoretical first 3 moments of spectrum

property q0

Long wavelength cutoff

property q1

Rolloff wavelength

property q2

Short wavelength cutoff

radialPSDMoment(self: tamaas._tamaas.Isopowerlaw2D, arg0: float) → float

Computes ∫ k^q ɸ(k) k dk from 0 to ∞

rmsHeights(self: tamaas._tamaas.Isopowerlaw2D) → float

Theoretical RMS of heights

rmsSlopes(self: tamaas._tamaas.Isopowerlaw2D) → float

Theoretical RMS of slopes

class tamaas._tamaas.Kato

Bases: ContactSolver

__init__(self: tamaas._tamaas.Kato, model: tamaas._tamaas.Model, surface: GridBaseWrap<T>, tolerance: float, mu: float) → None

addFunctionalTerm(self: tamaas._tamaas.ContactSolver, arg0: tamaas._tamaas.Functional) → None

Add a term to the contact functional to minimize

computeCost(self: tamaas._tamaas.Kato, use_tresca: bool = False) → float

property dump_freq

Frequency of displaying solver info

property functional

property max_iter

Maximum number of iterations

property model

setDumpFrequency(self: tamaas._tamaas.ContactSolver, dump_freq: int) → None

setMaxIterations(self: tamaas._tamaas.ContactSolver, max_iter: int) → None

solve(self: tamaas._tamaas.Kato, p0: List[float], proj_iter: int = 50) → None

solveRegularized(self: tamaas._tamaas.Kato, p0: GridBaseWrap<T>, r: float = 0.01) → float

solveRelaxed(self: tamaas._tamaas.Kato, g0: GridBaseWrap<T>) → float

property surface

property tolerance

Solver tolerance

class tamaas._tamaas.KatoSaturated

Bases: PolonskyKeerRey

Solver for pseudo-plasticity problems where the normal pressure is constrained above by a saturation pressure “pmax”

__init__(self: tamaas._tamaas.KatoSaturated, model: tamaas._tamaas.Model, surface: GridBaseWrap<T>, tolerance: float, pmax: float) → None

addFunctionalTerm(self: tamaas._tamaas.ContactSolver, arg0: tamaas._tamaas.Functional) → None

Add a term to the contact functional to minimize

computeError(self: tamaas._tamaas.PolonskyKeerRey) → float

property dump_freq

Frequency of displaying solver info

property functional

gap = <type.gap: 0>

property max_iter

Maximum number of iterations

property model

property pmax

Saturation normal pressure

pressure = <type.pressure: 1>

setDumpFrequency(self: tamaas._tamaas.ContactSolver, dump_freq: int) → None

setIntegralOperator(self: tamaas._tamaas.PolonskyKeerRey, arg0: str) → None

setMaxIterations(self: tamaas._tamaas.ContactSolver, max_iter: int) → None

solve(*args, **kwargs)

Overloaded function.

1. solve(self: tamaas._tamaas.ContactSolver, target_force: List[float]) -> float

Solve the contact for a mean traction/gap vector

2. solve(self: tamaas._tamaas.ContactSolver, target_normal_pressure: float) -> float

Solve the contact for a mean normal pressure/gap

property surface

property tolerance

Solver tolerance

class type

Bases: pybind11_object

Members:

gap

pressure

__init__(self: tamaas._tamaas.PolonskyKeerRey.type, value: int) → None

gap = <type.gap: 0>

property name

pressure = <type.pressure: 1>

property value

class tamaas._tamaas.LogLevel

Bases: pybind11_object

Members:

debug

info

warning

error

__init__(self: tamaas._tamaas.LogLevel, value: int) → None

debug = <LogLevel.debug: 0>

error = <LogLevel.error: 3>

info = <LogLevel.info: 1>

property name

property value

warning = <LogLevel.warning: 2>

class tamaas._tamaas.Logger

Bases: pybind11_object

__init__(self: tamaas._tamaas.Logger) → None

get(self: tamaas._tamaas.Logger, arg0: tamaas._tamaas.LogLevel) → tamaas._tamaas.Logger

Get a logger object for a log level

class tamaas._tamaas.MaugisAdhesionFunctional

Bases: AdhesionFunctional

Cohesive zone potential F = H(g - ρ)·γ/ρ

__init__(self: tamaas._tamaas.MaugisAdhesionFunctional, surface: GridBaseWrap<T>) → None

computeF(self: tamaas._tamaas.Functional, arg0: GridBaseWrap<T>, arg1: GridBaseWrap<T>) → float

Compute functional value

computeGradF(self: tamaas._tamaas.Functional, arg0: GridBaseWrap<T>, arg1: GridBaseWrap<T>) → None

Compute functional gradient

property parameters

Parameters dictionary

setParameters(self: tamaas._tamaas.AdhesionFunctional, arg0: Dict[str, float]) → None

class tamaas._tamaas.Model

Bases: FieldContainer

property E

Young’s modulus

property E_star

Contact (Hertz) modulus

__init__(self: tamaas._tamaas.Model, arg0: tamaas._tamaas.model_type, arg1: List[float], arg2: List[int]) → None

Create a new model of a given type, physical size and global discretization.

Parameters:

• model_type – the type of desired model

• system_size – the physical size of the domain in each direction

• global_discretization – number of points in each direction

addDumper(self: tamaas._tamaas.Model, dumper: tamaas::ModelDumper) → None

Register a dumper

applyElasticity(self: tamaas._tamaas.Model, arg0: numpy.ndarray[numpy.float64], arg1: numpy.ndarray[numpy.float64]) → None

Apply Hooke’s law

property be_engine

Boundary element engine

property boundary_fields

property boundary_shape

Number of points on boundary

property boundary_system_size

Physical size of surface

property displacement

Displacement field

dump(self: tamaas._tamaas.Model) → None

Write model data to registered dumpers

getBEEngine(self: tamaas._tamaas.Model) → tamaas._tamaas.BEEngine

getBoundaryDiscretization(self: tamaas._tamaas.Model) → List[int]

getBoundarySystemSize(self: tamaas._tamaas.Model) → List[float]

getDiscretization(self: tamaas._tamaas.Model) → List[int]

getDisplacement(self: tamaas._tamaas.Model) → GridBaseWrap<T>

getField(self: tamaas::Model, field_name: str) → GridVariant

getFields(self: tamaas::Model) → List[str]

Return fields list

getHertzModulus(self: tamaas._tamaas.Model) → float

getIntegralOperator(self: tamaas._tamaas.Model, operator_name: str) → tamaas::IntegralOperator

getPoissonRatio(self: tamaas._tamaas.Model) → float

getShearModulus(self: tamaas._tamaas.Model) → float

getSystemSize(self: tamaas._tamaas.Model) → List[float]

getTraction(self: tamaas._tamaas.Model) → GridBaseWrap<T>

getYoungModulus(self: tamaas._tamaas.Model) → float

property global_shape

Global discretization (in MPI environement)

property mu

Shear modulus

property nu

Poisson’s ratio

property operators

Returns a dict-like object allowing access to the model’s integral operators

registerField(self: tamaas::Model, field_name: str, field: numpy.ndarray[numpy.float64]) → None

setElasticity(self: tamaas._tamaas.Model, E: float, nu: float) → None

setIntegrationMethod(self: tamaas._tamaas.Model, arg0: tamaas::integration_method, arg1: float) → None

property shape

Discretization (local in MPI environment)

solveDirichlet(self: tamaas._tamaas.Model) → None

Solve surface displacemnts -> tractions

solveNeumann(self: tamaas._tamaas.Model) → None

Solve surface tractions -> displacements

property system_size

Size of physical domain

property traction

Surface traction field

property type

class tamaas._tamaas.ModelDumper

Bases: pybind11_object

__init__(self: tamaas._tamaas.ModelDumper) → None

dump(self: tamaas._tamaas.ModelDumper, model: tamaas._tamaas.Model) → None

Dump model

class tamaas._tamaas.ModelFactory

Bases: pybind11_object

__init__(*args, **kwargs)

static createModel(*args, **kwargs)

Overloaded function.

1. createModel(model_type: tamaas._tamaas.model_type, system_size: List[float], global_discretization: List[int]) -> tamaas._tamaas.Model

Create a new model of a given type, physical size and global discretization.

Parameters:

• model_type – the type of desired model

• system_size – the physical size of the domain in each direction

• global_discretization – number of points in each direction

2. createModel(model: tamaas._tamaas.Model) -> tamaas._tamaas.Model

Create a deep copy of a model.

static createResidual(model: tamaas._tamaas.Model, sigma_y: float, hardening: float = 0.0) → tamaas::Residual

Create an isotropic linear hardening residual. :param model: the model on which to define the residual :param sigma_y: the (von Mises) yield stress :param hardening: the hardening modulus

static registerHookeField(model: tamaas._tamaas.Model, name: str) → None

Register a HookeField operator

static registerNonPeriodic(model: tamaas._tamaas.Model, name: str) → None

Register non-periodic Boussinesq operator

static registerVolumeOperators(model: tamaas._tamaas.Model) → None

Register Boussinesq and Mindlin operators to model.

static setIntegrationMethod(operator: tamaas::IntegralOperator, method: tamaas::integration_method, cutoff: float) → None

Set the integration method (linear or cutoff) for a volume integral operator

exception tamaas._tamaas.ModelTypeError

Bases: TypeError

__init__(*args, **kwargs)

args

with_traceback()

Exception.with_traceback(tb) – set self.__traceback__ to tb and return self.

exception tamaas._tamaas.NotImplementedError

Bases: NotImplementedError

__init__(*args, **kwargs)

args

with_traceback()

Exception.with_traceback(tb) – set self.__traceback__ to tb and return self.

class tamaas._tamaas.PolonskyKeerRey

Bases: ContactSolver

Main solver class for normal elastic contact problems. Its functional can be customized to add an adhesion term, and its primal variable can be set to either the gap or the pressure.

__init__(self: tamaas._tamaas.PolonskyKeerRey, model: tamaas._tamaas.Model, surface: GridBaseWrap<T>, tolerance: float, primal_type: tamaas._tamaas.PolonskyKeerRey.type = <type.pressure: 1>, constraint_type: tamaas._tamaas.PolonskyKeerRey.type = <type.pressure: 1>) → None

addFunctionalTerm(self: tamaas._tamaas.ContactSolver, arg0: tamaas._tamaas.Functional) → None

Add a term to the contact functional to minimize

computeError(self: tamaas._tamaas.PolonskyKeerRey) → float

property dump_freq

Frequency of displaying solver info

property functional

gap = <type.gap: 0>

property max_iter

Maximum number of iterations

property model

pressure = <type.pressure: 1>

setDumpFrequency(self: tamaas._tamaas.ContactSolver, dump_freq: int) → None

setIntegralOperator(self: tamaas._tamaas.PolonskyKeerRey, arg0: str) → None

setMaxIterations(self: tamaas._tamaas.ContactSolver, max_iter: int) → None

solve(*args, **kwargs)

Overloaded function.

1. solve(self: tamaas._tamaas.ContactSolver, target_force: List[float]) -> float

Solve the contact for a mean traction/gap vector

2. solve(self: tamaas._tamaas.ContactSolver, target_normal_pressure: float) -> float

Solve the contact for a mean normal pressure/gap

property surface

property tolerance

Solver tolerance

class type

Bases: pybind11_object

Members:

gap

pressure

__init__(self: tamaas._tamaas.PolonskyKeerRey.type, value: int) → None

gap = <type.gap: 0>

property name

pressure = <type.pressure: 1>

property value

class tamaas._tamaas.PolonskyKeerTan

Bases: ContactSolver

__init__(self: tamaas._tamaas.PolonskyKeerTan, model: tamaas._tamaas.Model, surface: GridBaseWrap<T>, tolerance: float, mu: float) → None

addFunctionalTerm(self: tamaas._tamaas.ContactSolver, arg0: tamaas._tamaas.Functional) → None

Add a term to the contact functional to minimize

computeCost(self: tamaas._tamaas.PolonskyKeerTan, use_tresca: bool = False) → float

property dump_freq

Frequency of displaying solver info

property functional

property max_iter

Maximum number of iterations

property model

setDumpFrequency(self: tamaas._tamaas.ContactSolver, dump_freq: int) → None

setMaxIterations(self: tamaas._tamaas.ContactSolver, max_iter: int) → None

solve(self: tamaas._tamaas.PolonskyKeerTan, p0: List[float]) → float

solveTresca(self: tamaas._tamaas.PolonskyKeerTan, p0: GridBaseWrap<T>) → float

property surface

property tolerance

Solver tolerance

class tamaas._tamaas.RegularizedPowerlaw1D

Bases: Filter1D

Isotropic regularized powerlaw with a plateau extending to the size of the system

__init__(self: tamaas._tamaas.RegularizedPowerlaw1D) → None

computeFilter(self: tamaas._tamaas.Filter1D, arg0: GridWrap<T, dim>) → None

Compute the Fourier coefficient of the surface

property hurst

Hurst exponent

property q1

Rolloff wavelength

property q2

Short wavelength cutoff

class tamaas._tamaas.RegularizedPowerlaw2D

Bases: Filter2D

Isotropic regularized powerlaw with a plateau extending to the size of the system

__init__(self: tamaas._tamaas.RegularizedPowerlaw2D) → None

computeFilter(self: tamaas._tamaas.Filter2D, arg0: GridWrap<T, dim>) → None

Compute the Fourier coefficient of the surface

property hurst

Hurst exponent

property q1

Rolloff wavelength

property q2

Short wavelength cutoff

class tamaas._tamaas.Residual

Bases: pybind11_object

__init__(self: tamaas._tamaas.Residual, model: tamaas._tamaas.Model, material: tamaas::Material) → None

Create a residual object with a material. Defines the following residual equation:

ɛ - ∇N[σ(ɛ)] - ∇M[t] = 0

Where σ(ɛ) is the eigenstress associated with the constitutive law.

Parameters:

• model – the model on which to define the residual

• material – material object which defines a constitutive law

applyTangent(self: tamaas._tamaas.Residual, arg0: GridBaseWrap<T>, arg1: GridBaseWrap<T>, arg2: GridBaseWrap<T>) → None

computeResidual(self: tamaas._tamaas.Residual, arg0: GridBaseWrap<T>) → None

computeResidualDisplacement(self: tamaas._tamaas.Residual, arg0: GridBaseWrap<T>) → None

getStress(self: tamaas._tamaas.Residual) → GridWrap<T, dim>

getVector(self: tamaas._tamaas.Residual) → GridBaseWrap<T>

property material

property model

setIntegrationMethod(self: tamaas._tamaas.Residual, arg0: tamaas::integration_method, arg1: float) → None

updateState(self: tamaas._tamaas.Residual, arg0: GridBaseWrap<T>) → None

property vector

class tamaas._tamaas.SquaredExponentialAdhesionFunctional

Bases: AdhesionFunctional

Potential of the form F = -γ·exp(-0.5·(g/ρ)²)

__init__(self: tamaas._tamaas.SquaredExponentialAdhesionFunctional, surface: GridBaseWrap<T>) → None

computeF(self: tamaas._tamaas.Functional, arg0: GridBaseWrap<T>, arg1: GridBaseWrap<T>) → float

Compute functional value

computeGradF(self: tamaas._tamaas.Functional, arg0: GridBaseWrap<T>, arg1: GridBaseWrap<T>) → None

Compute functional gradient

property parameters

Parameters dictionary

setParameters(self: tamaas._tamaas.AdhesionFunctional, arg0: Dict[str, float]) → None

class tamaas._tamaas.Statistics1D

Bases: pybind11_object

__init__(*args, **kwargs)

static computeAutocorrelation(arg0: GridWrap<T, dim>) → GridWrap<T, dim>

Compute autocorrelation of surface

static computeFDRMSSlope(arg0: GridWrap<T, dim>) → float

Compute hrms’ with finite differences

static computeMoments(arg0: GridWrap<T, dim>) → List[float]

Compute spectral moments

static computePowerSpectrum(arg0: GridWrap<T, dim>) → GridWrap<T, dim>

Compute PSD of surface

static computeRMSHeights(arg0: GridWrap<T, dim>) → float

Compute hrms

static computeSpectralRMSSlope(arg0: GridWrap<T, dim>) → float

Compute hrms’ in Fourier space

static contact(tractions: GridWrap<T, dim>, perimeter: int = 0) → float

Compute the (corrected) contact area. Permieter is the total contact perimeter in number of segments.

static graphArea(zdisplacement: GridWrap<T, dim>) → float

Compute area defined by function graph.

class tamaas._tamaas.Statistics2D

Bases: pybind11_object

__init__(*args, **kwargs)

static computeAutocorrelation(arg0: GridWrap<T, dim>) → GridWrap<T, dim>

Compute autocorrelation of surface

static computeFDRMSSlope(arg0: GridWrap<T, dim>) → float

Compute hrms’ with finite differences

static computeMoments(arg0: GridWrap<T, dim>) → List[float]

Compute spectral moments

static computePowerSpectrum(arg0: GridWrap<T, dim>) → GridWrap<T, dim>

Compute PSD of surface

static computeRMSHeights(arg0: GridWrap<T, dim>) → float

Compute hrms

static computeSpectralRMSSlope(arg0: GridWrap<T, dim>) → float

Compute hrms’ in Fourier space

static contact(tractions: GridWrap<T, dim>, perimeter: int = 0) → float

Compute the (corrected) contact area. Permieter is the total contact perimeter in number of segments.

static graphArea(zdisplacement: GridWrap<T, dim>) → float

Compute area defined by function graph.

class tamaas._tamaas.SurfaceGenerator1D

Bases: pybind11_object

__init__(*args, **kwargs)

buildSurface(self: tamaas._tamaas.SurfaceGenerator1D) → GridWrap<T, dim>

Generate a surface and return a reference to it

property random_seed

Random generator seed

setRandomSeed(self: tamaas._tamaas.SurfaceGenerator1D, arg0: int) → None

setSizes(self: tamaas._tamaas.SurfaceGenerator1D, arg0: List[int[1]]) → None

property shape

Global shape of surfaces

class tamaas._tamaas.SurfaceGenerator2D

Bases: pybind11_object

__init__(*args, **kwargs)

buildSurface(self: tamaas._tamaas.SurfaceGenerator2D) → GridWrap<T, dim>

Generate a surface and return a reference to it

property random_seed

Random generator seed

setRandomSeed(self: tamaas._tamaas.SurfaceGenerator2D, arg0: int) → None

setSizes(self: tamaas._tamaas.SurfaceGenerator2D, arg0: List[int[2]]) → None

property shape

Global shape of surfaces

class tamaas._tamaas.SurfaceGeneratorFilter1D

Bases: SurfaceGenerator1D

Generates a rough surface with Gaussian noise in the PSD

__init__(*args, **kwargs)

Overloaded function.

1. __init__(self: tamaas._tamaas.SurfaceGeneratorFilter1D) -> None

Default constructor

2. __init__(self: tamaas._tamaas.SurfaceGeneratorFilter1D, arg0: List[int[1]]) -> None

Initialize with global surface shape

buildSurface(self: tamaas._tamaas.SurfaceGenerator1D) → GridWrap<T, dim>

Generate a surface and return a reference to it

property random_seed

Random generator seed

setFilter(self: tamaas._tamaas.SurfaceGeneratorFilter1D, filter: tamaas._tamaas.Filter1D) → None

Set PSD filter

setRandomSeed(self: tamaas._tamaas.SurfaceGenerator1D, arg0: int) → None

setSizes(self: tamaas._tamaas.SurfaceGenerator1D, arg0: List[int[1]]) → None

setSpectrum(self: tamaas._tamaas.SurfaceGeneratorFilter1D, filter: tamaas._tamaas.Filter1D) → None

Set PSD filter

property shape

Global shape of surfaces

property spectrum

Power spectrum object

class tamaas._tamaas.SurfaceGeneratorFilter2D

Bases: SurfaceGenerator2D

Generates a rough surface with Gaussian noise in the PSD

__init__(*args, **kwargs)

Overloaded function.

1. __init__(self: tamaas._tamaas.SurfaceGeneratorFilter2D) -> None

Default constructor

2. __init__(self: tamaas._tamaas.SurfaceGeneratorFilter2D, arg0: List[int[2]]) -> None

Initialize with global surface shape

buildSurface(self: tamaas._tamaas.SurfaceGenerator2D) → GridWrap<T, dim>

Generate a surface and return a reference to it

property random_seed

Random generator seed

setFilter(self: tamaas._tamaas.SurfaceGeneratorFilter2D, filter: tamaas._tamaas.Filter2D) → None

Set PSD filter

setRandomSeed(self: tamaas._tamaas.SurfaceGenerator2D, arg0: int) → None

setSizes(self: tamaas._tamaas.SurfaceGenerator2D, arg0: List[int[2]]) → None

setSpectrum(self: tamaas._tamaas.SurfaceGeneratorFilter2D, filter: tamaas._tamaas.Filter2D) → None

Set PSD filter

property shape

Global shape of surfaces

property spectrum

Power spectrum object

class tamaas._tamaas.SurfaceGeneratorRandomPhase1D

Bases: SurfaceGeneratorFilter1D

Generates a rough surface with uniformly distributed phases and exact prescribed PSD

__init__(*args, **kwargs)

Overloaded function.

1. __init__(self: tamaas._tamaas.SurfaceGeneratorRandomPhase1D) -> None

Default constructor

2. __init__(self: tamaas._tamaas.SurfaceGeneratorRandomPhase1D, arg0: List[int[1]]) -> None

Initialize with global surface shape

buildSurface(self: tamaas._tamaas.SurfaceGenerator1D) → GridWrap<T, dim>

Generate a surface and return a reference to it

property random_seed

Random generator seed

setFilter(self: tamaas._tamaas.SurfaceGeneratorFilter1D, filter: tamaas._tamaas.Filter1D) → None

Set PSD filter

setRandomSeed(self: tamaas._tamaas.SurfaceGenerator1D, arg0: int) → None

setSizes(self: tamaas._tamaas.SurfaceGenerator1D, arg0: List[int[1]]) → None

setSpectrum(self: tamaas._tamaas.SurfaceGeneratorFilter1D, filter: tamaas._tamaas.Filter1D) → None

Set PSD filter

property shape

Global shape of surfaces

property spectrum

Power spectrum object

class tamaas._tamaas.SurfaceGeneratorRandomPhase2D

Bases: SurfaceGeneratorFilter2D

Generates a rough surface with uniformly distributed phases and exact prescribed PSD

__init__(*args, **kwargs)

Overloaded function.

1. __init__(self: tamaas._tamaas.SurfaceGeneratorRandomPhase2D) -> None

Default constructor

2. __init__(self: tamaas._tamaas.SurfaceGeneratorRandomPhase2D, arg0: List[int[2]]) -> None

Initialize with global surface shape

buildSurface(self: tamaas._tamaas.SurfaceGenerator2D) → GridWrap<T, dim>

Generate a surface and return a reference to it

property random_seed

Random generator seed

setFilter(self: tamaas._tamaas.SurfaceGeneratorFilter2D, filter: tamaas._tamaas.Filter2D) → None

Set PSD filter

setRandomSeed(self: tamaas._tamaas.SurfaceGenerator2D, arg0: int) → None

setSizes(self: tamaas._tamaas.SurfaceGenerator2D, arg0: List[int[2]]) → None

setSpectrum(self: tamaas._tamaas.SurfaceGeneratorFilter2D, filter: tamaas._tamaas.Filter2D) → None

Set PSD filter

property shape

Global shape of surfaces

property spectrum

Power spectrum object

class tamaas._tamaas.TamaasInfo

Bases: pybind11_object

__init__(*args, **kwargs)

backend = 'cpp'

branch = ''

build_type = 'release'

commit = ''

diff = ''

has_mpi = False

has_petsc = False

remotes = ''

version = '2.7.1+45.g95040ce'

tamaas._tamaas.finalize() → None

tamaas._tamaas.get_log_level() → tamaas._tamaas.LogLevel

tamaas._tamaas.initialize(num_threads: int = 0) → None

Initialize tamaas with desired number of threads. Automatically called upon import of the tamaas module, but can be manually called to set the desired number of threads.

class tamaas._tamaas.integration_method

Bases: pybind11_object

Integration method used for the computation of volumetric Fourier operators

Members:

linear : No approximation error, O(N₁·N₂·N₃) time complexity, may cause float overflow/underflow

cutoff : Approximation, O(sqrt(N₁²+N₂²)·N₃²) time complexity, no overflow/underflow risk

__init__(self: tamaas._tamaas.integration_method, value: int) → None

cutoff = <integration_method.cutoff: 0>

linear = <integration_method.linear: 1>

property name

property value

class tamaas._tamaas.model_type

Bases: pybind11_object

Members:

basic_1d : Normal contact with 1D interface

basic_2d : Normal contact with 2D interface

surface_1d : Normal & tangential contact with 1D interface

surface_2d : Normal & tangential contact with 2D interface

volume_1d : Contact with volumetric representation and 1D interface

volume_2d : Contact with volumetric representation and 2D interface

__init__(self: tamaas._tamaas.model_type, value: int) → None

basic_1d = <model_type.basic_1d: 0>

basic_2d = <model_type.basic_2d: 1>

property name

surface_1d = <model_type.surface_1d: 2>

surface_2d = <model_type.surface_2d: 3>

property value

volume_1d = <model_type.volume_1d: 4>

volume_2d = <model_type.volume_2d: 5>

tamaas._tamaas.set_log_level(arg0: tamaas._tamaas.LogLevel) → None

tamaas._tamaas.to_voigt(arg0: GridWrap<T, dim>) → GridWrap<T, dim>

Convert a 3D tensor field to voigt notation

class tamaas._tamaas._DFSANESolver

Bases: EPSolver

__init__(*args, **kwargs)

Overloaded function.

1. __init__(self: tamaas._tamaas._DFSANESolver, residual: tamaas._tamaas.Residual) -> None

2. __init__(self: tamaas._tamaas._DFSANESolver, residual: tamaas._tamaas.Residual, model: tamaas._tamaas.Model) -> None

beforeSolve(self: tamaas._tamaas.EPSolver) → None

getResidual(self: tamaas._tamaas.EPSolver) → tamaas._tamaas.Residual

getStrainIncrement(self: tamaas._tamaas.EPSolver) → GridBaseWrap<T>

property max_iter

setToleranceManager(self: tamaas._tamaas.EPSolver, arg0: tamaas._tamaas._tolerance_manager) → None

solve(self: tamaas._tamaas.EPSolver) → None

property tolerance

updateState(self: tamaas._tamaas.EPSolver) → None

Module defining convenience MPI routines.

tamaas._tamaas.mpi.gather(arg0: GridWrap<T, dim>) → GridWrap<T, dim>

Gather 2D surfaces

tamaas._tamaas.mpi.global_shape(local_shape: List[int]) → List[int]

Gives the global shape of a 1D/2D local shape

tamaas._tamaas.mpi.local_offset(global_shape: List[int]) → int

Gives the local offset of a 1D/2D global shape

tamaas._tamaas.mpi.local_shape(global_shape: List[int]) → List[int]

Gives the local size of a 1D/2D global shape

tamaas._tamaas.mpi.rank() → int

Returns the rank of the local process

tamaas._tamaas.mpi.scatter(arg0: GridWrap<T, dim>) → GridWrap<T, dim>

Scatter 2D surfaces

class tamaas._tamaas.mpi.sequential

Bases: pybind11_object

__init__(self: tamaas._tamaas.mpi.sequential) → None

tamaas._tamaas.mpi.size() → int

Returns the number of MPI processes

Module defining basic computations on fields.

tamaas._tamaas.compute.deviatoric(model_type: tamaas._tamaas.model_type, deviatoric: GridWrap<T, dim>, field: GridWrap<T, dim>) → None

Compute the deviatoric part of a tensor field

tamaas._tamaas.compute.eigenvalues(model_type: tamaas._tamaas.model_type, eigenvalues_out: GridWrap<T, dim>, field: GridWrap<T, dim>) → None

Compute eigenvalues of a tensor field

tamaas._tamaas.compute.from_voigt(arg0: GridWrap<T, dim>) → GridWrap<T, dim>

Convert a 3D tensor field to voigt notation

tamaas._tamaas.compute.to_voigt(arg0: GridWrap<T, dim>) → GridWrap<T, dim>

Convert a 3D tensor field to voigt notation

tamaas._tamaas.compute.von_mises(model_type: tamaas._tamaas.model_type, von_mises: GridWrap<T, dim>, field: GridWrap<T, dim>) → None

Compute the Von Mises invariant of a tensor field

Tamaas Dumpers for Model

Dumpers for the class Model.

class tamaas.dumpers.JSONDumper(file_descriptor: Union[str, PathLike[str], IOBase])

Bases: ModelDumper

Dumper to JSON.

__init__(file_descriptor: Union[str, PathLike[str], IOBase])

Construct with file handle.

dump(model: Model)

Dump model.

classmethod read(fd: IO[str])

Read model from file.

class tamaas.dumpers.FieldDumper(basename: Union[str, PathLike[str]], *fields, **kwargs)

Bases: ModelDumper

Abstract dumper for python classes using fields.

extension = ''

name_format = '{basename}{postfix}.{extension}'

__init__(basename: Union[str, PathLike[str]], *fields, **kwargs)

Construct with desired fields.

add_field(field: str)

Add another field to the dump.

get_fields(model: Model)

Get the desired fields.

dump(model: Model)

Dump model.

classmethod read(file_descriptor: Union[str, PathLike[str], IOBase])

Read model from file.

classmethod read_sequence(glob_pattern)

Read models from a file sequence.

property file_path

Get the default filename.

class tamaas.dumpers.NumpyDumper(basename: Union[str, PathLike[str]], *fields, **kwargs)

Bases: FieldDumper

Dumper to compressed numpy files.

extension = 'npz'

classmethod read(file_descriptor: Union[str, PathLike[str], IOBase])

Create model from Numpy file.

__init__(basename: Union[str, PathLike[str]], *fields, **kwargs)

Construct with desired fields.

add_field(field: str)

Add another field to the dump.

dump(model: Model)

Dump model.

property file_path

Get the default filename.

get_fields(model: Model)

Get the desired fields.

name_format = '{basename}{postfix}.{extension}'

classmethod read_sequence(glob_pattern)

Read models from a file sequence.

class tamaas.dumpers.H5Dumper(basename: Union[str, PathLike[str]], *fields, **kwargs)

Bases: FieldDumper

Dumper to HDF5 file format.

extension = 'h5'

__init__(basename: Union[str, PathLike[str]], *fields, **kwargs)

Construct with desired fields.

classmethod read(file_descriptor: Union[str, PathLike[str], IOBase])

Create model from HDF5 file.

add_field(field: str)

Add another field to the dump.

dump(model: Model)

Dump model.

property file_path

Get the default filename.

get_fields(model: Model)

Get the desired fields.

name_format = '{basename}{postfix}.{extension}'

classmethod read_sequence(glob_pattern)

Read models from a file sequence.

class tamaas.dumpers.UVWDumper(basename: Union[str, PathLike[str]], *fields, **kwargs)

Bases: FieldDumper

Dumper to VTK files for elasto-plastic calculations.

extension = 'vtr'

__init__(basename: Union[str, PathLike[str]], *fields, **kwargs)

Construct with desired fields.

add_field(field: str)

Add another field to the dump.

dump(model: Model)

Dump model.

property file_path

Get the default filename.

get_fields(model: Model)

Get the desired fields.

name_format = '{basename}{postfix}.{extension}'

classmethod read(file_descriptor: Union[str, PathLike[str], IOBase])

Read model from file.

classmethod read_sequence(glob_pattern)

Read models from a file sequence.

class tamaas.dumpers.UVWGroupDumper(basename: Union[str, PathLike[str]], *fields, **kwargs)

Bases: FieldDumper

Dumper to ParaViewData files.

extension = 'pvd'

__init__(basename: Union[str, PathLike[str]], *fields, **kwargs)

Construct with desired fields.

add_field(field: str)

Add another field to the dump.

dump(model: Model)

Dump model.

property file_path

Get the default filename.

get_fields(model: Model)

Get the desired fields.

name_format = '{basename}{postfix}.{extension}'

classmethod read(file_descriptor: Union[str, PathLike[str], IOBase])

Read model from file.

classmethod read_sequence(glob_pattern)

Read models from a file sequence.

Tamaas Nonlinear solvers

Nonlinear solvers for plasticity problems.

Solvers in this module use scipy.optimize to solve the implicit non-linear equation for plastic deformations with fixed contact pressures.

exception tamaas.nonlinear_solvers.NLNoConvergence

Bases: RuntimeError

Convergence not reached exception.

__init__(*args, **kwargs)

args

with_traceback()

Exception.with_traceback(tb) – set self.__traceback__ to tb and return self.

class tamaas.nonlinear_solvers.DFSANESolver(residual, model=None, callback=None)

Bases: ScipySolver

Solve using a spectral residual jacobianless method.

See doi:10.1090/S0025-5718-06-01840-0 for details on method and the relevant Scipy documentation for details on parameters.

__init__(residual, model=None, callback=None)

Construct nonlinear solver with residual.

Parameters:

• residual – plasticity residual object

• model – Deprecated

• callback – passed on to the Scipy solver

beforeSolve(self: tamaas._tamaas.EPSolver) → None

getResidual(self: tamaas._tamaas.EPSolver) → tamaas._tamaas.Residual

getStrainIncrement(self: tamaas._tamaas.EPSolver) → GridBaseWrap<T>

reset()

Set solution vector to zero.

setToleranceManager(self: tamaas._tamaas.EPSolver, arg0: tamaas._tamaas._tolerance_manager) → None

solve()

Solve R(δε) = 0 using a Scipy function.

property tolerance

updateState(self: tamaas._tamaas.EPSolver) → None

tamaas.nonlinear_solvers.DFSANECXXSolver

alias of _DFSANESolver

class tamaas.nonlinear_solvers.NewtonKrylovSolver(residual, model=None, callback=None)

Bases: ScipySolver

Solve using a finite-difference Newton-Krylov method.

__init__(residual, model=None, callback=None)

Construct nonlinear solver with residual.

Parameters:

• residual – plasticity residual object

• model – Deprecated

• callback – passed on to the Scipy solver

beforeSolve(self: tamaas._tamaas.EPSolver) → None

getResidual(self: tamaas._tamaas.EPSolver) → tamaas._tamaas.Residual

getStrainIncrement(self: tamaas._tamaas.EPSolver) → GridBaseWrap<T>

reset()

Set solution vector to zero.

setToleranceManager(self: tamaas._tamaas.EPSolver, arg0: tamaas._tamaas._tolerance_manager) → None

solve()

Solve R(δε) = 0 using a Scipy function.

property tolerance

updateState(self: tamaas._tamaas.EPSolver) → None

tamaas.nonlinear_solvers.ToleranceManager(start, end, rate)

Decorate solver to manage tolerance of non-linear solve step.

Tamaas utilities

Convenience utilities.

tamaas.utils.log_context(log_level: LogLevel)

Context manager to easily control Tamaas’ logging level.

tamaas.utils.publications(format_str='{pub.citation}\n\t{pub.doi}')

Print publications associated with objects in use.

tamaas.utils.load_path(solver: ContactSolver, loads: Iterable[Union[float, ndarray]], verbose: bool = False, callback=None) → Iterable[Model]

Generate model objects solutions for a sequence of applied loads.

Parameters:

• solver – a contact solver object

• loads – an iterable sequence of loads

• verbose – print info output of solver

• callback – a callback executed after the yield

tamaas.utils.seeded_surfaces(generator: Union[SurfaceGenerator1D, SurfaceGenerator2D], seeds: Iterable[int]) → Iterable[ndarray]

Generate rough surfaces with a prescribed seed sequence.

Parameters:

• generator – surface generator object

• seeds – random seed sequence

tamaas.utils.hertz_surface(system_size: Iterable[float], shape: Iterable[int], radius: float) → ndarray

Construct a parabolic surface.

Parameters:

• system_size – size of the domain in each direction

• shape – number of points in each direction

• radius – radius of surface

tamaas.utils.radial_average(x: ndarray, y: ndarray, values: ndarray, r: ndarray, theta: ndarray, method: str = 'linear', endpoint: bool = False) → ndarray

Compute the radial average of a 2D field.

Averages radially for specified r values. See scipy.interpolate.RegularGridInterpolator for more details.

C++ API

template<typename Iterator>
struct acc_range

#include <accumulator.hh>

Range for convenience.

Public Functions

inline Iterator begin() const

inline Iterator end() const

Public Members

Iterator _begin

Iterator _end

template<model_type type, typename Source, typename = std::enable_if_t<is_proxy<Source>::value>>
class Accumulator

#include <accumulator.hh>

Accumulation integral manager.

Public Types

enum class direction

Direction flag.

Values:

enumerator forward

enumerator backward

Public Functions

inline Accumulator()

Constructor.

inline void makeUniformMesh(UInt N, Real domain_size)

Initialize uniform mesh.

inline const std::vector<Real> &nodePositions() const

inline acc_range<iterator<direction::forward>> forward(std::vector<BufferType> &nvalues, const Grid<Real, trait::boundary_dimension> &wvectors)

Prepare forward loop.

inline acc_range<iterator<direction::backward>> backward(std::vector<BufferType> &nvalues, const Grid<Real, trait::boundary_dimension> &wvectors)

Prepare backward loop.

inline void reset(std::vector<BufferType> &nvalues, const Grid<Real, trait::boundary_dimension> &wvectors)

inline std::vector<BufferType> &nodeValues()

inline const Grid<Real, trait::boundary_dimension> &waveVectors()

inline auto elements()

Create a range over the elements in the mesh.

Private Types

using trait = model_type_traits<type>

using BufferType = GridHermitian<Real, trait::boundary_dimension>

Private Members

std::array<BufferType, 2> accumulator

std::vector<Real> node_positions

std::vector<BufferType> *node_values

const Grid<Real, trait::boundary_dimension> *wavevectors

class AdhesionFunctional : public tamaas::functional::Functional

#include <adhesion_functional.hh>

Functional class for adhesion energy.

Subclassed by tamaas::functional::ExponentialAdhesionFunctional, tamaas::functional::MaugisAdhesionFunctional, tamaas::functional::SquaredExponentialAdhesionFunctional

Public Functions

inline const std::map<std::string, Real> &getParameters() const

Get parameters.

inline void setParameters(std::map<std::string, Real> other)

Set parameters.

Protected Functions

inline AdhesionFunctional(const GridBase<Real> &surface)

Constructor.

Protected Attributes

GridBase<Real> surface

std::map<std::string, Real> parameters

class AndersonMixing : public tamaas::EPICSolver

#include <anderson.hh>

Public Functions

AndersonMixing(ContactSolver &csolver, EPSolver &epsolver, Real tolerance = 1e-10, UInt memory = 5)

virtual Real solve(const std::vector<Real> &load) override

Private Types

using memory_t = std::deque<GridBase<Real>>

Private Members

UInt M

Private Static Functions

static std::vector<Real> computeGamma(const memory_t &residual)

static GridBase<Real> mixingUpdate(GridBase<Real> x, std::vector<Real> gamma, const memory_t &memory, const memory_t &residual_memory, Real relaxation)

template<size_t nargs>
struct Apply

#include <apply.hh>

Helper function for application of a functor on a thrust::tuple.

Public Static Functions

template<typename Functor, typename Tuple, typename ...Args>
static inline auto apply(Functor &&func, Tuple &&t, Args&&... args) -> decltype(Apply<nargs - 1>::apply(std::forward<Functor>(func), std::forward<Tuple>(t), thrust::get<nargs - 1>(t), std::forward<Args>(args)...))

template<>
struct Apply<0>

#include <apply.hh>

Public Static Functions

template<typename Functor, typename Tuple, typename ...Args>
static inline auto apply(Functor &&func, Tuple&&, Args&&... args) -> decltype(func(std::forward<Args>(args)...))

template<typename Functor, typename ret_type = void>
class ApplyFunctor

#include <apply.hh>

Helper class for functor application in thrust.

Public Functions

inline ApplyFunctor(const Functor &functor)

inline ApplyFunctor(const ApplyFunctor &o)

template<typename Tuple>
inline ret_type operator()(Tuple &&t) const

Private Members

const Functor &functor

template<typename T>
class arange

#include <loop.hh>

Helper class to count iterations within lambda-loop.

Public Types

using it_type = thrust::counting_iterator<T>

using reference = typename it_type::reference

Public Functions

inline arange(T start, T size)

inline it_type begin(UInt = 1) const

inline it_type end(UInt = 1) const

inline UInt getNbComponents() const

Private Members

T start

T range_size

template<typename T>
struct Array

#include <array.hh>

Generic storage class with wrapping capacities.

Public Functions

Array() = default

Default.

inline Array(UInt size)

Empty array of given size.

inline Array(const Array &v)

Copy constructor (deep)

inline Array(Array &&v) noexcept

Move constructor (transfers data ownership)

inline Array(T *data, UInt size) noexcept

Wrap array on data.

inline Array(span<T> view) noexcept

Wrap on span.

inline ~Array()

Destructor.

inline Array &operator=(const Array &v)

Copy operator.

inline Array &operator=(Array &&v) noexcept

Move operator.

inline Array &operator=(span<T> v) noexcept

Wrap on view.

inline void wrap(const Array &other) noexcept

Wrap array.

inline void wrap(span<T> view) noexcept

Wrap view.

inline void wrap(T *data, UInt size) noexcept

Wrap a memory pointer.

inline const T *data() const

Data pointer access (const)

inline T *data()

Data pointer access (non-const)

inline void resize(UInt new_size, const T &value = T())

Resize array.

inline void reserve(UInt size)

Reserve storage space.

inline T &operator[](UInt i)

Access operator.

inline const T &operator[](UInt i) const

Access operator (const)

inline UInt size() const

Get size of array.

inline span<T> view() const

Private Members

span<T> view_

span<T>::size_type reserved_ = 0

bool wrapped_ = false

Allocator<T> alloc_

class assertion_error : public invalid_argument

#include <errors.hh>

class BeckTeboulle : public tamaas::Kato

#include <beck_teboulle.hh>

Public Functions

BeckTeboulle(Model &model, const GridBase<Real> &surface, Real tolerance, Real mu)

Constructor.

virtual Real solve(std::vector<Real> g0) override

Solve.

Private Functions

template<model_type type>
Real solveTmpl(GridBase<Real> &g0)

Template for solve function.

class BEEngine

#include <be_engine.hh>

Boundary equation engine class. Solves the Neumann/Dirichlet problem This class should be dimension and model-type agnostic.

Subclassed by tamaas::BEEngineTmpl< type >

Public Functions

inline BEEngine(Model *model)

virtual ~BEEngine() = default

Destructor.

virtual void solveNeumann(GridBase<Real> &neumann, GridBase<Real> &dirichlet) const = 0

Solve Neumann problem (expects boundary data)

virtual void solveDirichlet(GridBase<Real> &dirichlet, GridBase<Real> &neumann) const = 0

Solve Dirichlet problem (expects boundary data)

virtual void registerNeumann() = 0

Register neumann operator.

virtual void registerDirichlet() = 0

Register dirichlet operator.

inline const Model &getModel() const

Get model.

inline Real getNeumannNorm()

Compute L_2 norm of influence functions.

Protected Attributes

Model *model

std::map<IntegralOperator::kind, std::shared_ptr<IntegralOperator>> operators

template<model_type type>
class BEEngineTmpl : public tamaas::BEEngine

#include <be_engine.hh>

Public Functions

inline BEEngineTmpl(Model *model)

virtual void solveNeumann(GridBase<Real> &neumann, GridBase<Real> &dirichlet) const override

Solve Neumann problem (expects boundary data)

virtual void solveDirichlet(GridBase<Real> &dirichlet, GridBase<Real> &neumann) const override

Solve Dirichlet problem (expects boundary data)

virtual void registerNeumann() override

Register neumann operator.

virtual void registerDirichlet() override

Register dirichlet operator.

template<UInt m, UInt j>
struct boundary_fft_helper

Public Static Functions

template<typename Buffer, typename Out>
static inline void backwardTransform(FFTEngine &e, Buffer &&buffer, Out &&out)

template<UInt m>
struct boundary_fft_helper<m, m>

Public Static Functions

template<typename Buffer, typename Out>
static inline void backwardTransform(FFTEngine &e, Buffer &&buffer, Out &&out)

template<model_type type, UInt derivative>
class Boussinesq : public tamaas::VolumePotential<type>

#include <boussinesq.hh>

Boussinesq tensor.

Public Functions

Boussinesq(Model *model)

Constructor.

virtual void apply(GridBase<Real> &source, GridBase<Real> &out) const override

Apply the Boussinesq operator.

Protected Functions

void initialize(UInt source_components, UInt out_components)

Private Types

using trait = model_type_traits<type>

using parent = VolumePotential<type>

template<UInt dim, UInt derivative_order>
class Boussinesq

#include <influence.hh>

Class for the Boussinesq tensor.

template<>
class Boussinesq<3, 0>

#include <influence.hh>

Subclassed by tamaas::influence::Boussinesq< 3, 1 >

Public Functions

inline Boussinesq(Real mu, Real nu)

Constructor.

template<bool apply_q_power = false, typename ST>
inline Vector<Complex, dim> applyU0(const StaticVector<Complex, ST, dim> &t, const VectorProxy<const Real, dim - 1> &q) const

template<bool apply_q_power = false, typename ST>
inline Vector<Complex, dim> applyU1(const StaticVector<Complex, ST, dim> &t, const VectorProxy<const Real, dim - 1> &q) const

Protected Attributes

const Real mu

const Real nu

const Real lambda

Protected Static Attributes

static constexpr UInt dim = 3

static constexpr UInt order = 0

template<>
class Boussinesq<3, 1> : protected tamaas::influence::Boussinesq<3, 0>

#include <influence.hh>

Boussinesq first gradient.

Public Functions

template<bool apply_q_power = false, typename ST>
inline Matrix<Complex, dim, dim> applyU0(const StaticVector<Complex, ST, dim> &t, const VectorProxy<const Real, dim - 1> &q) const

template<bool apply_q_power = false, typename ST>
inline Matrix<Complex, dim, dim> applyU1(const StaticVector<Complex, ST, dim> &t, const VectorProxy<const Real, dim - 1> &q) const

Protected Types

using parent = Boussinesq<3, 0>

Protected Static Attributes

static constexpr UInt dim = parent::dim

static constexpr UInt order = parent::order + 1

template<model_type type, typename boussinesq_t>
struct BoussinesqHelper

#include <boussinesq_helper.hh>

Public Types

using trait = model_type_traits<type>

using BufferType = GridHermitian<Real, bdim>

using source_t = typename KelvinTrait<boussinesq_t>::source_t

using out_t = typename KelvinTrait<boussinesq_t>::out_t

Public Functions

template<bool apply_q_power>
inline void apply(BufferType &tractions, std::vector<BufferType> &out, const Grid<Real, bdim> &wavevectors, Real domain_size, const boussinesq_t &boussinesq)

template<bool apply_q_power>
inline void apply(BufferType &tractions, BufferType &out, UInt layer, const Grid<Real, bdim> &wavevectors, UInt discretization, Real domain_size, const boussinesq_t &boussinesq)

inline void makeFundamentalModeGreatAgain(BufferType&, std::vector<BufferType>&, influence::ElasticHelper<dim>&)

template<typename ST>
inline void makeFundamentalModeGreatAgain(StaticVector<Complex, ST, dim>&, out_t&, influence::ElasticHelper<dim>&)

Public Static Attributes

static constexpr UInt dim = trait::dimension

static constexpr UInt bdim = trait::boundary_dimension

Protected Attributes

Accumulator<type, source_t> accumulator

really only here for mesh

template<UInt dim>
class Cluster

#include <flood_fill.hh>

Public Functions

Cluster(Point start, const Grid<bool, dim> &map, Grid<bool, dim> &visited, bool diagonal)

Constructor.

Cluster(const Cluster &other)

Copy constructor.

Cluster() = default

Default constructor.

inline UInt getArea() const

Get area of cluster.

inline UInt getPerimeter() const

Get perimeter of cluster.

inline const auto &getPoints() const

Get contact points.

BBox boundingBox() const

Get bounding box.

std::array<Int, dim> extent() const

Get bounding box extent.

auto getNextNeighbors(const std::array<Int, dim> &p)

Assign next neighbors.

auto getDiagonalNeighbors(const std::array<Int, dim> &p)

Assign diagonal neighbors.

auto getNextNeighbors(const std::array<Int, 1> &p)

auto getDiagonalNeighbors(const std::array<Int, 1>&)

auto getNextNeighbors(const std::array<Int, 2> &p)

auto getDiagonalNeighbors(const std::array<Int, 2> &p)

auto getNextNeighbors(const std::array<Int, 3> &p)

auto getDiagonalNeighbors(const std::array<Int, 3> &p)

Private Types

using Point = std::array<Int, dim>

using BBox = std::pair<std::array<Int, dim>, std::array<Int, dim>>

Private Members

std::vector<Point> points

List of points in the cluster.

UInt perimeter = 0

Perimeter size (number of segments)

struct comm

#include <mpi_interface.hh>

Public Functions

inline operator MPI_Comm() const

Public Members

MPI_Comm _comm

Public Static Functions

static comm &world()

template<class Compute_t>
class ComputeOperator : public tamaas::IntegralOperator

Public Functions

inline ComputeOperator(Model *model)

Constructor.

inline virtual IntegralOperator::kind getKind() const override

Kind.

inline virtual model_type getType() const override

Type.

inline virtual void updateFromModel() override

Update any data dependent on model parameters.

inline virtual void apply(GridBase<Real> &in, GridBase<Real> &out) const override

Apply functor.

class Condat : public tamaas::Kato

#include <condat.hh>

Public Functions

Condat(Model &model, const GridBase<Real> &surface, Real tolerance, Real mu)

Constructor.

virtual Real solve(std::vector<Real> p0) override

Solve.

template<model_type type>
Real solveTmpl(GridBase<Real> &p0, Real grad_step)

Template for solve function.

template<UInt comp>
void updateGap(Real sigma, Real grad_step, GridBase<Real> &q)

Update gap.

template<UInt comp>
void updateLagrange(GridBase<Real> &q, GridBase<Real> &p0)

Update Lagrange multiplier q.

inline void setGradStep(Real gstep)

Private Members

std::unique_ptr<GridBase<Real>> pressure_old = nullptr

Real grad_step = 0.9

class ContactSolver

#include <contact_solver.hh>

Subclassed by tamaas::Kato, tamaas::PolonskyKeerRey

Public Functions

ContactSolver(Model &model, const GridBase<Real> &surface, Real tolerance)

Constructor.

virtual ~ContactSolver() = default

Destructor.

virtual void printState(UInt iter, Real cost_f, Real error) const

Print state of solve.

virtual void logIteration(UInt iter, Real cost_f, Real error) const

Log iteration info.

inline auto getMaxIterations() const

Get maximum number of iterations.

inline void setMaxIterations(UInt n)

Set maximum number of iterations.

inline auto getDumpFrequency() const

Get dump_frequency.

inline void setDumpFrequency(UInt n)

Set dump_frequency.

void addFunctionalTerm(std::shared_ptr<functional::Functional> func)

Add term to functional.

inline const functional::Functional &getFunctional() const

Returns functional object.

void setFunctional(std::shared_ptr<functional::Functional> func)

Sets functional sum to a single term.

inline virtual Real solve(std::vector<Real>)

Solve for a mean traction vector.

inline virtual Real solve(Real load)

Solve for normal pressure.

TAMAAS_ACCESSOR(tolerance, Real, Tolerance)

Accessor for tolerance.

inline GridBase<Real> &getSurface()

inline Model &getModel()

Protected Attributes

Model &model

GridBase<Real> surface

std::shared_ptr<GridBase<Real>> _gap = nullptr

functional::MetaFunctional functional

Real tolerance

UInt max_iterations = 1000

Real surface_stddev

UInt dump_frequency = 100

class CuFFTEngine : public tamaas::FFTEngine

#include <cufft_engine.hh>

Public Functions

inline explicit CuFFTEngine(unsigned int flags = FFTW_ESTIMATE) noexcept

Initialize with flags.

inline virtual void forward(const Grid<Real, 1> &real, GridHermitian<Real, 1> &spectral) override

Execute a forward plan on real and spectral 1D.

inline virtual void forward(const Grid<Real, 2> &real, GridHermitian<Real, 2> &spectral) override

Execute a forward plan on real and spectral 2D.

inline virtual void backward(Grid<Real, 1> &real, GridHermitian<Real, 1> &spectral) override

Execute a backward plan on real and spectral 1D.

inline virtual void backward(Grid<Real, 2> &real, GridHermitian<Real, 2> &spectral) override

Execute a backward plan on real and spectral 2D.

inline unsigned int flags() const

Public Static Functions

static inline auto cast(Complex *data)

Cast to FFTW complex type.

static inline auto cast(const Complex *data)

Protected Attributes

unsigned int _flags

FFTW flags.

std::map<key_t, plan_t> plans

plans corresponding to signatures

Private Types

using plan_t = std::pair<cufft::plan, cufft::plan>

Private Functions

template<UInt dim>
void forwardImpl(const Grid<Real, dim> &real, GridHermitian<Real, dim> &spectral)

Perform forward (R2C) transform.

template<UInt dim>
void backwardImpl(Grid<Real, dim> &real, const GridHermitian<Real, dim> &spectral)

Perform backward (C2R) transform.

plan_t &getPlans(key_t key)

Return the plans pair for a given transform signature.

template<bool upper>
struct cutoff_functor

#include <kelvin_helper.hh>

Public Functions

inline void operator()(VectorProxy<const Real, bdim> qv, source_t wj0, source_t wj1, out_t out_i) const

Public Members

Real r

Real xc

Real dx

Real cutoff

kelvin_t kelvin

class DCFFT : public tamaas::Westergaard<model_type::basic_2d, IntegralOperator::neumann>

#include <dcfft.hh>

Non-periodic Boussinesq operator, computed with padded FFT.

Public Functions

DCFFT(Model *model)

virtual void apply(GridBase<Real> &input, GridBase<Real> &output) const override

Apply influence coefficients in Fourier domain.

Private Types

using trait = model_type_traits<model_type::basic_2d>

Private Functions

void initInfluence()

Init influence with real-space square patch solution.

Private Members

mutable Grid<Real, bdim> extended_buffer

Private Static Attributes

static constexpr UInt dim = trait::dimension

static constexpr UInt bdim = trait::boundary_dimension

static constexpr UInt comp = trait::components

template<UInt derivative>
struct derivative_traits

#include <volume_potential.hh>

Trait type for component management.

template<>
struct derivative_traits<0>

#include <volume_potential.hh>

Public Static Attributes

template<model_type type>
static constexpr UInt source_components = model_type_traits<type>::components

template<model_type type>
static constexpr UInt out_components = model_type_traits<type>::components

template<>
struct derivative_traits<1>

#include <volume_potential.hh>

Public Static Attributes

template<model_type type>
static constexpr UInt source_components = model_type_traits<type>::voigt

template<model_type type>
static constexpr UInt out_components = model_type_traits<type>::components

template<>
struct derivative_traits<2>

#include <volume_potential.hh>

Public Static Attributes

template<model_type type>
static constexpr UInt source_components = model_type_traits<type>::voigt

template<model_type type>
static constexpr UInt out_components = model_type_traits<type>::voigt

struct Deviatoric

#include <computes.hh>

Compute deviatoric of tensor field.

Public Static Functions

template<UInt dim>
static inline void call(Grid<Real, dim> &dev, const Grid<Real, dim> &field)

class DFSANESolver : public tamaas::EPSolver

#include <dfsane_solver.hh>

Derivative-free non-linear solver.

This algorithm is based on W. La Cruz, J. Martínez, and M. Raydan, “Spectral residual method without gradient information for solving large-scale nonlinear systems of equations,” Math. Comp., vol. 75, no. 255, pp. 1429–1448, 2006, doi: 10.1090/S0025-5718-06-01840-0.

The same algorithm is available in scipy.optimize, but this version is robustly parallel by default (i.e. does not depend on BLAS’s parallelism and is future-proof for MPI parallelism).

Public Functions

DFSANESolver(Residual &residual)

virtual void solve() override

TAMAAS_ACCESSOR(max_iterations, UInt, MaxIterations)

Protected Functions

Real computeSpectralCoeff(const std::pair<Real, Real> &bounds)

void computeSearchDirection(Real sigma)

void lineSearch(Real eta_k)

Protected Attributes

GridBase<Real> search_direction

GridBase<Real> previous_residual

GridBase<Real> current_x

GridBase<Real> delta_x

GridBase<Real> delta_residual

std::deque<Real> previous_merits

std::function<Real(UInt)> eta

UInt max_iterations = 100

Protected Static Functions

static Real computeAlpha(Real alpha, Real f, Real fk, const std::pair<Real, Real> &bounds)

struct Eigenvalues

#include <computes.hh>

Compute eigenvalues of a symmetric matrix field.

Public Static Functions

template<UInt dim>
static inline void call(Grid<Real, dim> &eigs, const Grid<Real, dim> &field)

class ElasticFunctional : public tamaas::functional::Functional

#include <elastic_functional.hh>

Generic functional for elastic energy.

Subclassed by tamaas::functional::ElasticFunctionalGap, tamaas::functional::ElasticFunctionalPressure

Public Functions

inline ElasticFunctional(const IntegralOperator &op, const GridBase<Real> &surface)

Protected Attributes

const IntegralOperator &op

GridBase<Real> surface

mutable std::unique_ptr<GridBase<Real>> buffer

class ElasticFunctionalGap : public tamaas::functional::ElasticFunctional

#include <elastic_functional.hh>

Functional with gap as primal field.

Public Functions

virtual Real computeF(GridBase<Real> &gap, GridBase<Real> &dual) const override

Compute functional with input gap.

virtual void computeGradF(GridBase<Real> &gap, GridBase<Real> &gradient) const override

Compute functional gradient with input gap.

inline ElasticFunctional(const IntegralOperator &op, const GridBase<Real> &surface)

class ElasticFunctionalPressure : public tamaas::functional::ElasticFunctional

#include <elastic_functional.hh>

Functional with pressure as primal field.

Public Functions

virtual Real computeF(GridBase<Real> &pressure, GridBase<Real> &dual) const override

Compute functional with input pressure.

virtual void computeGradF(GridBase<Real> &pressure, GridBase<Real> &gradient) const override

Compute functional gradient with input pressure.

inline ElasticFunctional(const IntegralOperator &op, const GridBase<Real> &surface)

template<UInt dim>
struct ElasticHelper

#include <influence.hh>

Functor to apply Hooke’s tensor.

Public Functions

inline ElasticHelper(Real mu, Real nu)

template<typename DT, typename ST>
inline Matrix<std::remove_cv_t<DT>, dim, dim> operator()(const StaticMatrix<DT, ST, dim, dim> &gradu) const

template<typename DT, typename ST>
inline SymMatrix<std::remove_cv_t<DT>, dim> operator()(const StaticSymMatrix<DT, ST, dim> &eps) const

template<typename DT, typename ST>
inline Matrix<std::remove_cv_t<DT>, dim, dim> inverse(const StaticMatrix<DT, ST, dim, dim> &sigma) const

Public Members

const Real mu

const Real nu

const Real lambda

class EPICSolver

#include <epic.hh>

Subclassed by tamaas::AndersonMixing

Public Functions

EPICSolver(ContactSolver &csolver, EPSolver &epsolver, Real tolerance = 1e-10, Real relaxation = 0.3)

Constructor.

virtual Real solve(const std::vector<Real> &load)

Real acceleratedSolve(const std::vector<Real> &load)

Real computeError(const GridBase<Real> &current, const GridBase<Real> &prev, Real factor) const

void fixedPoint(GridBase<Real> &result, const GridBase<Real> &x, const GridBase<Real> &initial_surface, std::vector<Real> load)

template<model_type type>
void setViews()

TAMAAS_ACCESSOR(tolerance, Real, Tolerance)

TAMAAS_ACCESSOR(relaxation, Real, Relaxation)

TAMAAS_ACCESSOR(max_iterations, UInt, MaxIterations)

inline const Model &getModel() const

Protected Attributes

GridBase<Real> surface

corrected surface

GridBase<Real> pressure

current pressure

std::unique_ptr<GridBase<Real>> residual_disp

plastic residual disp

std::unique_ptr<GridBase<Real>> pressure_inc

pressure increment

ContactSolver &csolver

EPSolver &epsolver

Real tolerance

Real relaxation

UInt max_iterations = 1000

class EPSolver

#include <ep_solver.hh>

Subclassed by tamaas::DFSANESolver, tamaas::PETScSolver

Public Functions

EPSolver(Residual &residual)

Constructor.

virtual ~EPSolver() = default

Destructor.

virtual void solve() = 0

virtual void updateState()

virtual void beforeSolve()

inline GridBase<Real> &getStrainIncrement()

inline Residual &getResidual()

inline Real getTolerance() const

inline void setTolerance(Real tol)

inline void setToleranceManager(ToleranceManager manager)

Protected Attributes

std::shared_ptr<GridBase<Real>> _x

Residual &_residual

ToleranceManager abs_tol = {1e-9, 1e-9, 1}

class Exception : public exception

#include <tamaas.hh>

Generic exception class.

Public Functions

inline Exception(std::string mesg)

Constructor.

inline const char *what() const noexcept override

~Exception() override = default

Private Members

std::string msg

message of exception

class ExponentialAdhesionFunctional : public tamaas::functional::AdhesionFunctional

#include <adhesion_functional.hh>

Exponential adhesion functional.

Public Functions

inline ExponentialAdhesionFunctional(const GridBase<Real> &surface)

Explicit declaration of constructor for swig.

virtual Real computeF(GridBase<Real> &gap, GridBase<Real> &pressure) const override

Compute the total adhesion energy.

virtual void computeGradF(GridBase<Real> &gap, GridBase<Real> &gradient) const override

Compute the gradient of the adhesion functional.

template<UInt interpolation_order>
struct ExponentialElement

#include <element.hh>

template<>
struct ExponentialElement<1>

#include <element.hh>

Public Static Functions

template<UInt shape>
static inline constexpr expolit::Polynomial<Real, 1> shapes()

static inline constexpr auto sign(bool upper)

template<bool upper, UInt shape>
static inline constexpr auto g0(Real q)

template<bool upper, UInt shape>
static inline constexpr auto g1(Real q)

class FFTEngine

#include <fft_engine.hh>

Subclassed by tamaas::CuFFTEngine, tamaas::FFTWEngine

Public Functions

virtual ~FFTEngine() noexcept = default

virtual void forward(const Grid<Real, 1> &real, GridHermitian<Real, 1> &spectral) = 0

Execute a forward plan on real and spectral 1D.

virtual void forward(const Grid<Real, 2> &real, GridHermitian<Real, 2> &spectral) = 0

Execute a forward plan on real and spectral 2D.

virtual void backward(Grid<Real, 1> &real, GridHermitian<Real, 1> &spectral) = 0

Execute a backward plan on real and spectral 1D.

virtual void backward(Grid<Real, 2> &real, GridHermitian<Real, 2> &spectral) = 0

Execute a backward plan on real and spectral 2D.

Public Static Functions

template<typename T, UInt dim, bool hermitian>
static Grid<T, dim> computeFrequencies(const std::array<UInt, dim> &sizes)

Fill a grid with wavevector values in appropriate ordering.

template<UInt dim>
static std::vector<std::array<UInt, dim>> realCoefficients(const std::array<UInt, dim> &sizes)

Return the grid indices that contain real coefficients (see R2C transform)

static std::unique_ptr<FFTEngine> makeEngine(unsigned int flags = FFTW_ESTIMATE)

Instanciate an appropriate FFTEngine subclass.

template<>
static std::vector<std::array<UInt, 2>> realCoefficients(const std::array<UInt, 2> &local_sizes)

template<>
static std::vector<std::array<UInt, 1>> realCoefficients(const std::array<UInt, 1> &local_sizes)

Protected Types

using key_t = std::basic_string<UInt>

Protected Static Functions

template<UInt dim>
static key_t make_key(const Grid<Real, dim> &real, const GridHermitian<Real, dim> &spectral)

Make a transform signature from a pair of grids.

template<typename T>
struct FFTWAllocator

#include <fftw_allocator.hh>

Class allocating SIMD aligned memory

Public Static Functions

static inline span<T> allocate(typename span<T>::size_type n) noexcept

Allocate memory.

static inline void deallocate(span<T> view) noexcept

Free memory.

class FFTWEngine : public tamaas::FFTEngine

#include <fftw_engine.hh>

Subclassed by tamaas::FFTWMPIEngine

Public Functions

inline explicit FFTWEngine(unsigned int flags = FFTW_ESTIMATE) noexcept

Initialize with flags.

inline virtual void forward(const Grid<Real, 1> &real, GridHermitian<Real, 1> &spectral) override

Execute a forward plan on real and spectral 1D.

inline virtual void forward(const Grid<Real, 2> &real, GridHermitian<Real, 2> &spectral) override

Execute a forward plan on real and spectral 2D.

inline virtual void backward(Grid<Real, 1> &real, GridHermitian<Real, 1> &spectral) override

Execute a backward plan on real and spectral 1D.

inline virtual void backward(Grid<Real, 2> &real, GridHermitian<Real, 2> &spectral) override

Execute a backward plan on real and spectral 2D.

inline unsigned int flags() const

Public Static Functions

static inline auto cast(Complex *data)

Cast to FFTW complex type.

static inline auto cast(const Complex *data)

Protected Types

using plan_t = std::pair<fftw::plan<Real>, fftw::plan<Real>>

using complex_t = fftw::helper<Real>::complex

Protected Functions

template<UInt dim>
void forwardImpl(const Grid<Real, dim> &real, GridHermitian<Real, dim> &spectral)

Perform forward (R2C) transform.

template<UInt dim>
void backwardImpl(Grid<Real, dim> &real, const GridHermitian<Real, dim> &spectral)

Perform backward (C2R) transform.

plan_t &getPlans(key_t key)

Return the plans pair for a given transform signature.

Protected Attributes

unsigned int _flags

FFTW flags.

std::map<key_t, plan_t> plans

plans corresponding to signatures

class FFTWMPIEngine : public tamaas::FFTWEngine

#include <fftw_mpi_engine.hh>

Public Functions

inline virtual void forward(const Grid<Real, 1>&, GridHermitian<Real, 1>&) override

Execute a forward plan on real and spectral 1D.

inline virtual void backward(Grid<Real, 1>&, GridHermitian<Real, 1>&) override

Execute a backward plan on real and spectral 1D.

virtual void forward(const Grid<Real, 2> &real, GridHermitian<Real, 2> &spectral) override

FFTW/MPI forward (r2c) transform.

virtual void backward(Grid<Real, 2> &real, GridHermitian<Real, 2> &spectral) override

FFTW/MPI backward (c2r) transform.

inline explicit FFTWEngine(unsigned int flags = FFTW_ESTIMATE) noexcept

Initialize with flags.

Protected Functions

plan_t &getPlans(key_t key)

Return the plans pair for a given transform signature.

Protected Attributes

std::map<key_t, Grid<Real, 2>> workspaces

Buffer for real data because of FFTW/MPI layout.

Protected Static Functions

static key_t make_key(const Grid<Real, 2> &real, const GridHermitian<Real, 2> &spectral)

Make a transform signature from a pair of grids.

static auto local_size(const key_t &key)

Get FFTW local sizes from an hermitian grid.

struct FieldContainer

#include <field_container.hh>

Subclassed by tamaas::IntegralOperator, tamaas::Model

Public Types

using Key = std::string

template<class T>
using GridBasePtr = std::shared_ptr<GridBase<T>>

using Value = boost::variant<GridBasePtr<Real>, GridBasePtr<UInt>, GridBasePtr<Int>, GridBasePtr<Complex>, GridBasePtr<bool>>

using FieldsMap = std::unordered_map<Key, Value>

Public Functions

virtual ~FieldContainer() = default

Destructor.

inline const Value &at(const Key &name) const

Access field pointer in const context.

inline Value &operator[](const Key &name)

Access/insert new pointer.

template<class T>
inline auto &field(const Key &name)

Access field of given type (non-const)

template<class T>
inline const auto &field(const Key &name) const

Access field of given type (const)

inline decltype(auto) fields() const

Return field keys.

inline const auto &fields_map() const

Return pointer map to fields.

template<model_type type, bool boundary, typename T, template<typename, UInt> class GridType = Grid, class Container = void>
inline std::shared_ptr<GridType<T, detail::dim_choice<type, boundary>::value>> request(const Key &name, Container &&n, UInt nc)

Return a field with given dimension, create if not in container.

template<bool boundary, typename T, typename Container>
inline decltype(auto) request(const Key &name, model_type type, Container &&n, UInt nc)

Return a field with given dimension, create if not in container.

Private Members

FieldsMap fields_

template<UInt dim>
class Filter

#include <filter.hh>

Subclassed by tamaas::Isopowerlaw< dim >, tamaas::RegularizedPowerlaw< dim >

Public Functions

Filter() = default

Default constructor.

virtual ~Filter() = default

Destructor.

virtual void computeFilter(GridHermitian<Real, dim> &filter_coefficients) const = 0

Compute Filter coefficients.

Protected Functions

template<typename T>
void computeFilter(T &&f, GridHermitian<Real, dim> &filter) const

Compute filter coefficients using lambda.

class FloodFill

#include <flood_fill.hh>

Public Static Functions

static List<1> getSegments(const Grid<bool, 1> &map)

Return a list of connected segments.

static List<2> getClusters(const Grid<bool, 2> &map, bool diagonal)

Return a list of connected areas.

static List<3> getVolumes(const Grid<bool, 3> &map, bool diagonal)

Return a list of connected volumes.

Private Types

template<UInt dim>
using List = std::vector<Cluster<dim>>

template<template<typename> class Trait, typename ...T>
struct fold_trait : public tamaas::detail::fold_trait_tail_rec<true, Trait, T...>

#include <tamaas.hh>

template<bool acc, template<typename> class Trait, typename Head, typename ...Tail>
struct fold_trait_tail_rec : public std::integral_constant<bool, fold_trait_tail_rec<acc and Trait<Head>::value, Trait, Tail...>::value>

#include <tamaas.hh>

template<bool acc, template<typename> class Trait, typename Head>
struct fold_trait_tail_rec<acc, Trait, Head> : public std::integral_constant<bool, acc and Trait<Head>::value>

#include <tamaas.hh>

class Functional

#include <functional.hh>

Generic functional class for the cost function of the optimization problem.

Subclassed by tamaas::functional::AdhesionFunctional, tamaas::functional::ElasticFunctional, tamaas::functional::MetaFunctional

Public Functions

virtual ~Functional() = default

Destructor.

virtual Real computeF(GridBase<Real> &variable, GridBase<Real> &dual) const = 0

Compute functional.

virtual void computeGradF(GridBase<Real> &variable, GridBase<Real> &gradient) const = 0

Compute functional gradient.

template<UInt N, UInt... ns>
struct get : public detail::get_rec<N, ns...>

#include <static_types.hh>

template<UInt n, UInt... ns>
struct get_rec<0, n, ns...> : public std::integral_constant<UInt, n>

#include <static_types.hh>

template<typename T, UInt dim>
class Grid : public tamaas::GridBase<T>

#include <grid.hh>

Multi-dimensional & multi-component array class.

This class is a container for multi-component data stored on a multi- dimensional grid.

The access function is the parenthesis operator. For a grid of dimension d, the operator takes d+1 arguments: the first d arguments are the position on the grid and the last one is the component of the stored data.

It is also possible to use the access operator with only one argument, it is then considering the grid as a flat array, accessing the given cell of the array.

Public Types

using value_type = T

using reference = value_type&

Public Functions

Grid()

Constructor by default (empty array)

template<typename RandomAccessIterator>
Grid(RandomAccessIterator begin, RandomAccessIterator end, UInt nb_components)

Constructor with shape from iterators.

template<typename RandomAccessIterator>
Grid(RandomAccessIterator begin, RandomAccessIterator end, UInt nb_components, span<value_type> data)

Construct with shape from iterators on data view.

template<typename Container>
inline Grid(Container &&n, UInt nb_components)

Constructor with container as shape.

template<typename Container>
inline Grid(Container &&n, UInt nb_components, span<value_type> data)

Constructor with shape and wrapped data.

inline Grid(const std::initializer_list<UInt> &n, UInt nb_components)

Constructor with initializer list.

inline Grid(const Grid &o)

Copy constructor.

inline Grid(Grid &&o) noexcept

Move constructor (transfers data ownership)

~Grid() override = default

Destructor.

void resize(const std::array<UInt, dim> &n)

Resize array.

void resize(const std::vector<UInt> &n)

Resize array (from std::vector)

void resize(std::initializer_list<UInt> n)

Resize array (from initializer list)

template<typename ForwardIt>
void resize(ForwardIt begin, ForwardIt end)

Resize array (from iterators)

inline UInt computeSize() const

Compute size.

inline virtual UInt getDimension() const override

Get grid dimension.

void computeStrides()

Compute strides.

virtual void printself(std::ostream &str) const

Print.

inline const std::array<UInt, dim> &sizes() const

Get sizes.

inline const std::array<UInt, dim + 1> &getStrides() const

Get strides.

template<typename ...T1>
inline std::enable_if_t<is_valid_index<T1...>::value, T&> operator()(T1... args)

Variadic access operator (non-const)

template<typename ...T1>
inline std::enable_if_t<is_valid_index<T1...>::value, const T&> operator()(T1... args) const

Variadic access operator.

template<std::size_t tdim>
inline T &operator()(std::array<UInt, tdim> tuple)

Tuple index access operator.

template<std::size_t tdim>
inline const T &operator()(std::array<UInt, tdim> tuple) const

Grid &operator=(const Grid &other)

Grid &operator=(Grid &&other) noexcept

template<typename T1>
void copy(const Grid<T1, dim> &other)

template<typename T1>
void move(Grid<T1, dim> &&other) noexcept

template<typename Container>
inline void wrap(GridBase<T> &other, Container &&n)

template<typename Container>
inline void wrap(const GridBase<T> &other, Container &&n)

inline void wrap(Grid &other)

inline void wrap(const Grid &other)

Public Static Attributes

static constexpr UInt dimension = dim

Protected Attributes

std::array<UInt, dim> n

shape of grid: size per dimension

std::array<UInt, dim + 1> strides

strides for access

Private Types

template<typename ...D>
using is_valid_index = fold_trait<std::is_integral, D...>

Private Functions

template<typename Container>
void init(const Container &n, UInt nb_components)

Init from standard container.

template<typename ...T1>
inline UInt unpackOffset(UInt offset, UInt index_pos, UInt index, T1... rest) const

Unpacking the arguments of variadic ()

template<typename ...T1>
inline UInt unpackOffset(UInt offset, UInt index_pos, UInt index) const

End case for recursion.

template<std::size_t tdim>
inline UInt computeOffset(std::array<UInt, tdim> tuple) const

Computing offset for a tuple index.

template<typename T>
class GridBase

#include <grid_base.hh>

Dimension agnostic grid with components stored per points.

Subclassed by tamaas::Grid< T, dim >

Public Types

using iterator = iterator_::iterator<T>

using const_iterator = iterator_::iterator<const T>

using value_type = T

using reference = value_type&

Public Functions

GridBase() = default

Constructor by default.

inline GridBase(const GridBase &o)

Copy constructor.

inline GridBase(GridBase &&o) noexcept

Move constructor (transfers data ownership)

inline explicit GridBase(UInt nb_points, UInt nb_components = 1)

Initialize with size.

virtual ~GridBase() = default

Destructor.

inline virtual UInt getDimension() const

Get grid dimension.

inline const T *getInternalData() const

Get internal data pointer (const)

inline T *getInternalData()

Get internal data pointer (non-const)

inline UInt getNbComponents() const

Get number of components.

inline void setNbComponents(UInt n)

Set number of components.

inline virtual UInt dataSize() const

Get total size.

inline UInt globalDataSize() const

Get global data size.

inline UInt getNbPoints() const

Get number of points.

inline UInt getGlobalNbPoints() const

Get global number of points.

void uniformSetComponents(const GridBase<T> &vec)

Set components.

inline void resize(UInt size)

Resize.

inline void reserve(UInt size)

Reserve storage w/o changing data logic.

inline virtual iterator begin(UInt n = 1)

inline virtual iterator end(UInt n = 1)

inline virtual const_iterator begin(UInt n = 1) const

inline virtual const_iterator end(UInt n = 1) const

inline decltype(auto) view() const

inline T &operator()(UInt i)

inline const T &operator()(UInt i) const

template<typename T1>
GridBase &operator+=(const GridBase<T1> &other)

template<typename T1>
GridBase &operator*=(const GridBase<T1> &other)

template<typename T1>
GridBase &operator-=(const GridBase<T1> &other)

template<typename T1>
GridBase &operator/=(const GridBase<T1> &other)

template<typename T1>
T dot(const GridBase<T1> &other) const

inline GridBase &operator+=(const T &e)

inline GridBase &operator*=(const T &e)

inline GridBase &operator-=(const T &e)

inline GridBase &operator/=(const T &e)

inline GridBase &operator=(const T &e)

template<typename DT, typename ST, UInt size>
GridBase &operator+=(const StaticArray<DT, ST, size> &b)

template<typename DT, typename ST, UInt size>
GridBase &operator-=(const StaticArray<DT, ST, size> &b)

template<typename DT, typename ST, UInt size>
GridBase &operator*=(const StaticArray<DT, ST, size> &b)

template<typename DT, typename ST, UInt size>
GridBase &operator/=(const StaticArray<DT, ST, size> &b)

template<typename DT, typename ST, UInt size>
GridBase &operator=(const StaticArray<DT, ST, size> &b)

inline T min() const

inline T max() const

inline T sum() const

inline T mean() const

inline T var() const

inline T l2norm() const

inline GridBase &operator=(const GridBase &o)

inline GridBase &operator=(GridBase &o)

inline GridBase &operator=(GridBase &&o) noexcept

template<typename T1>
inline void copy(const GridBase<T1> &other)

template<typename T1>
inline void move(GridBase<T1> &&other) noexcept

inline GridBase &wrap(GridBase &o)

inline GridBase &wrap(const GridBase &o)

template<typename T1>
inline GridBase<T> &operator+=(const GridBase<T1> &other)

template<typename T1>
inline GridBase<T> &operator-=(const GridBase<T1> &other)

template<typename T1>
inline GridBase<T> &operator*=(const GridBase<T1> &other)

template<typename T1>
inline GridBase<T> &operator/=(const GridBase<T1> &other)

template<typename DT, typename ST, UInt size>
GridBase<T> &operator+=(const StaticArray<DT, ST, size> &b)

template<typename DT, typename ST, UInt size>
GridBase<T> &operator-=(const StaticArray<DT, ST, size> &b)

template<typename DT, typename ST, UInt size>
GridBase<T> &operator*=(const StaticArray<DT, ST, size> &b)

template<typename DT, typename ST, UInt size>
GridBase<T> &operator/=(const StaticArray<DT, ST, size> &b)

template<typename DT, typename ST, UInt size>
GridBase<T> &operator=(const StaticArray<DT, ST, size> &b)

Protected Attributes

Array<T> data

UInt nb_components = 1

template<typename T, UInt dim>
class GridHermitian : public tamaas::Grid<complex<T>, dim>

#include <grid_hermitian.hh>

Multi-dimensional, multi-component herimitian array.

This class represents an array of hermitian data, meaning it has dimensions of: n1 * n2 * n3 * … * (nx / 2 + 1)

However, it acts as a fully dimensioned array, returning a dummy reference for data outside its real dimension, allowing one to write full (and inefficient) loops without really worrying about the reduced dimension.

It would however be better to just use the true dimensions of the surface for all intents and purposes, as it saves computation time.

Public Types

using value_type = complex<T>

Public Functions

GridHermitian() = default

GridHermitian(const GridHermitian &o) = default

GridHermitian(GridHermitian &&o) noexcept = default

template<typename ...T1>
inline complex<T> &operator()(T1... args)

template<typename ...T1>
inline const complex<T> &operator()(T1... args) const

Public Static Functions

static inline std::array<UInt, dim> hermitianDimensions(std::array<UInt, dim> n)

template<typename Int, typename = std::enable_if_t<std::is_arithmetic<Int>::value>>
static inline std::vector<Int> hermitianDimensions(std::vector<Int> n)

Private Functions

template<typename ...T1>
inline void packTuple(UInt *t, UInt i, T1... args) const

template<typename ...T1>
inline void packTuple(UInt *t, UInt i) const

template<template<typename, UInt> class Base, typename T, UInt base_dim, UInt dim>
class GridView : public Base<T, dim>

#include <grid_view.hh>

View type on grid This is a view on a contiguous chunk of data defined by a grid.

Public Types

using iterator = typename Base<T, dim>::iterator

using const_iterator = typename Base<T, dim>::const_iterator

using value_type = typename Base<T, dim>::value_type

using referecence = typename Base<T, dim>::reference

Public Functions

GridView(GridBase<typename Base<T, dim>::value_type> &grid_base, const std::vector<UInt> &multi_index, Int component = -1)

Constructor.

inline GridView(GridView &&o) noexcept

Move constructor.

~GridView() override = default

Destructor.

inline UInt dataSize() const override

void reserve(UInt size) = delete

void resize(UInt size) = delete

inline iterator begin(UInt = 1) override

Iterators.

inline iterator end(UInt = 1) override

inline const_iterator begin(UInt = 1) const override

inline const_iterator end(UInt = 1) const override

Protected Attributes

Base<T, base_dim> *grid

template<typename T>
struct helper

#include <interface_impl.hh>

Allocation helper for different float types.

template<>
struct helper<double>

#include <interface_impl.hh>

Public Types

using complex = fftw_complex

using plan = fftw_plan

Public Static Functions

static inline auto alloc_real(std::size_t size)

static inline auto alloc_complex(std::size_t size)

template<>
struct helper<float>

#include <interface_impl.hh>

Public Types

using complex = fftwf_complex

using plan = fftwf_plan

Public Static Functions

static inline auto alloc_real(std::size_t size)

static inline auto alloc_complex(std::size_t size)

template<>
struct helper<long double>

#include <interface_impl.hh>

Public Types

using complex = fftwl_complex

using plan = fftwl_plan

Public Static Functions

static inline auto alloc_real(std::size_t size)

static inline auto alloc_complex(std::size_t size)

template<model_type type>
class Hooke : public tamaas::IntegralOperator

#include <hooke.hh>

Applies Hooke’s law of elasticity.

Subclassed by tamaas::HookeField< type >

Public Functions

inline virtual model_type getType() const override

Type of underlying model.

inline virtual IntegralOperator::kind getKind() const override

Operator is local in real space.

inline virtual void updateFromModel() override

Does not update.

virtual void apply(GridBase<Real> &strain, GridBase<Real> &stress) const override

Apply Hooke’s tensor.

virtual std::pair<UInt, UInt> matvecShape() const override

LinearOperator shape.

virtual GridBase<Real> matvec(GridBase<Real> &X) const override

LinearOperator interface.

inline IntegralOperator(Model *model)

Constructor.

template<model_type type>
class HookeField : public tamaas::Hooke<type>

#include <hooke.hh>

Public Functions

HookeField(Model *model)

virtual void apply(GridBase<Real> &strain, GridBase<Real> &stress) const override

Apply Hooke’s tensor.

template<UInt dim>
struct HookeFieldHelper

Public Functions

inline void operator()(MatrixProxy<Real, dim, dim> sigma, MatrixProxy<const Real, dim, dim> epsilon, const Real &mu, const Real &nu)

Public Members

influence::ElasticHelper<dim> elasticity = {0, 0}

class IntegralOperator : public tamaas::FieldContainer

#include <integral_operator.hh>

Generic class for integral operators.

Subclassed by tamaas::detail::ComputeOperator< Compute_t >, tamaas::Hooke< type >, tamaas::VolumePotential< type >, tamaas::Westergaard< mtype, otype >, tamaas::Westergaard< model_type::basic_2d, IntegralOperator::neumann >

Public Types

enum kind

Kind of operator.

Values:

enumerator neumann

enumerator dirichlet

enumerator dirac

Public Functions

inline IntegralOperator(Model *model)

Constructor.

virtual void apply(GridBase<Real> &input, GridBase<Real> &output) const = 0

Apply operator on input.

inline virtual void applyIf(GridBase<Real> &input, GridBase<Real> &output, const std::function<bool(UInt)>&) const

Apply operator on filtered input.

inline virtual void updateFromModel()

Update any data dependent on model parameters.

inline const Model &getModel() const

Get model.

inline virtual kind getKind() const

Kind.

virtual model_type getType() const

Type.

inline virtual Real getOperatorNorm()

Norm.

inline virtual std::pair<UInt, UInt> matvecShape() const

Dense shape (for Scipy integration)

inline virtual GridBase<Real> matvec(GridBase<Real>&) const

matvec definition

Protected Attributes

Model *model = nullptr

template<UInt interpolation_order>
class Integrator

#include <integrator.hh>

Public Static Functions

template<bool upper, UInt shape>
static inline Real G0(Real q, Real r, Real xc)

Standard integral of \(\exp(\pm qy) \phi(y)\) over an element of radius \(r\) and center \(x_c\)

template<bool upper, UInt shape>
static inline Real G1(Real q, Real r, Real xc)

Standard integral of \(qy\exp(\pm qy) \phi(y)\) over an element of radius \(r\) and center \(x_c\)

template<UInt shape>
static inline constexpr Real F(Real r)

Standard integral of \(\phi(y)\) over an element of radius \(r\) and center \(x_c\). Used for fundamental mode

Private Types

using element = ExponentialElement<interpolation_order>

Private Static Attributes

static constexpr std::pair<Real, Real> bounds = {-1, 1}

template<typename T, UInt dim>
struct Internal

#include <internal.hh>

Public Functions

inline void initialize()

Initialize previous field.

inline void update()

Update the field previous state.

inline void reset()

Reset the current field.

inline void operator=(decltype(field) &&field)

Assign the field pointer.

inline decltype(field) ::element_type & operator* ()

Dereference the field pointer.

inline const decltype(field) ::element_type & operator* () const

Dereference the field pointer (const version)

inline operator std::shared_ptr<GridBase<T>>()

Upcast to GridBase pointer.

Public Members

std::shared_ptr<Grid<T, dim>> field

Stored field.

decltype(field) previous

template<typename T>
struct is_arithmetic : public std::is_arithmetic<T>

#include <static_types.hh>

template<typename T>
struct is_arithmetic<complex<T>> : public true_type

#include <static_types.hh>

template<typename T>
struct is_policy : public false_type

#include <loop.hh>

template<>
struct is_policy<const thrust::detail::device_t&> : public true_type

#include <loop.hh>

template<>
struct is_policy<const thrust::detail::device_t> : public true_type

#include <loop.hh>

template<>
struct is_policy<const thrust::detail::host_t&> : public true_type

#include <loop.hh>

template<>
struct is_policy<const thrust::detail::host_t> : public true_type

#include <loop.hh>

template<>
struct is_policy<thrust::detail::device_t> : public true_type

#include <loop.hh>

template<>
struct is_policy<thrust::detail::host_t> : public true_type

#include <loop.hh>

template<class Type>
struct is_proxy : public false_type

#include <static_types.hh>

template<typename T, UInt n, UInt m>
struct is_proxy<MatrixProxy<T, n, m>> : public true_type

#include <static_types.hh>

template<typename T, UInt n>
struct is_proxy<SymMatrixProxy<T, n>> : public true_type

#include <static_types.hh>

template<template<typename, typename, UInt...> class StaticParent, typename T, UInt... dims>
struct is_proxy<TensorProxy<StaticParent, T, dims...>> : public true_type

#include <static_types.hh>

template<typename T, UInt n>
struct is_proxy<VectorProxy<T, n>> : public true_type

#include <static_types.hh>

template<typename Container>
struct is_valid_container : public std::is_same<std::remove_cv_t<std::decay_t<Container>::value_type>, std::remove_cv_t<ValueType>>

#include <ranges.hh>

template<UInt dim>
class Isopowerlaw : public tamaas::Filter<dim>

#include <isopowerlaw.hh>

Class representing an isotropic power law spectrum.

Public Functions

virtual void computeFilter(GridHermitian<Real, dim> &filter_coefficients) const override

Compute filter coefficients.

inline Real operator()(const VectorProxy<Real, dim> &q_vec) const

Compute a point of the PSD.

Real rmsHeights() const

Analytical rms of heights.

std::vector<Real> moments() const

Analytical moments.

Real alpha() const

Analytical Nayak’s parameter.

Real rmsSlopes() const

Analytical RMS slopes.

Real radialPSDMoment(Real q) const

Computes ∫ k^q ɸ(k) k dk from 0 to ∞

Real elasticEnergy() const

Compute full contact energy (unscaled by E*)

TAMAAS_ACCESSOR(q0, UInt, Q0)

TAMAAS_ACCESSOR(q1, UInt, Q1)

TAMAAS_ACCESSOR(q2, UInt, Q2)

TAMAAS_ACCESSOR(hurst, Real, Hurst)

Real radialPSDMoment(Real q) const

Real radialPSDMoment(Real) const

Protected Attributes

UInt q0

UInt q1

UInt q2

Real hurst

class IsotropicHardening : public tamaas::Material

#include <isotropic_hardening.hh>

Public Functions

IsotropicHardening(Model *model, Real sigma_0, Real h)

Constructor.

void computeInelasticDeformationIncrement(View &increment, const View &strain, const View &strain_increment)

Compute plastic strain increment with radial return algorithm.

void computeStress(Field &stress, const Field &strain, const Field &strain_increment) override

Compute stress.

void computeEigenStress(Field &stress, const Field &strain, const Field &strain_increment) override

Compute stress due to plastic strain increment.

virtual void update() override

Update internal variables.

void applyTangent(Field &output, const Field &input, const Field &strain, const Field &strain_increment) override

inline Real getHardeningModulus() const

inline Real getYieldStress() const

inline const GridBase<Real> &getPlasticStrain() const

inline GridBase<Real> &getPlasticStrain()

inline void setHardeningModulus(Real h_)

inline void setYieldStress(Real sigma_0_)

Public Static Functions

static inline Real hardening(Real p, Real h, Real sigma_0)

Linear hardening function.

Protected Attributes

Real sigma_0

Real h

< initial yield stress

Internal<Real, dim> plastic_strain

< hardening modulus

Internal<Real, dim> cumulated_plastic_strain

Private Types

using parent = Material

using trait = model_type_traits<type>

using Field = typename parent::Field

using Mat = SymMatrixProxy<Real, dim>

using CMat = SymMatrixProxy<const Real, dim>

using View = Grid<Real, dim>

Private Static Attributes

static constexpr auto type = model_type::volume_2d

static constexpr UInt dim = trait::dimension

template<typename T>
class iterator

#include <iterator.hh>

Subclassed by tamaas::iterator_::iterator_view< T >

Public Types

using value_type = T

using difference_type = std::ptrdiff_t

using pointer = T*

using reference = T&

using iterator_category = thrust::random_access_device_iterator_tag

Public Functions

inline iterator(pointer data, difference_type step_size)

constructor

inline iterator(const iterator &o)

copy constructor

inline iterator(iterator &&o) noexcept

move constructor

template<typename U, typename = std::enable_if_t<std::is_convertible<T, U>::value>>
inline iterator(const iterator<U> &o)

copy from a different qualified type

template<typename U, typename = std::enable_if_t<std::is_convertible<T, U>::value>>
inline iterator(iterator<U> &&o)

move from a different qualified type

inline iterator &operator=(const iterator &o)

inline iterator &operator=(iterator &&o) noexcept

inline reference operator*()

dereference iterator

inline reference operator*() const

dereference iterator

inline iterator &operator+=(difference_type a)

increment with given offset

inline iterator &operator++()

increment iterator

inline bool operator<(const iterator &a) const

comparison

inline bool operator!=(const iterator &a) const

inequality

inline bool operator==(const iterator &a) const

equality

inline difference_type operator-(const iterator &a) const

needed for OpenMP range calculations

inline void setStep(difference_type s)

Protected Attributes

T *data

difference_type step

Friends

friend class iterator

class iterator : public tamaas::iterator_::iterator<ValueType>

#include <ranges.hh>

Public Types

using value_type = LocalType

using reference = value_type

Public Functions

inline iterator(const parent &o)

inline reference operator*()

inline reference operator*() const

Private Types

using parent = iterator_::iterator<ValueType>

template<direction dir>
struct iterator

#include <accumulator.hh>

Forward/Backward iterator for integration passes.

Public Types

using integ = Integrator<1>

Public Functions

inline iterator(Accumulator &acc, Int k)

Constructor.

inline iterator(const iterator &o)

Copy constructor.

inline bool operator!=(const iterator &o) const

Compare.

inline iterator &operator++()

Increment.

inline std::tuple<Int, Real, BufferType&, BufferType&> operator*()

Dereference iterator (TODO uniformize tuple types)

Public Static Attributes

static constexpr bool upper = dir == direction::backward

Protected Functions

inline bool setup()

Update index layer and element info.

inline void next()

Set current layer and update element index.

Protected Attributes

Accumulator &acc

Int k = 0

accumulator holder

element index

Int l = 0

layer index

Real r = 0

element radius

Real xc = 0

element center

Protected Static Functions

static inline Int layer(Int element)

Element index => layer index.

static inline Int nextElement(Int element)

Next element index in right direction.

template<typename T>
class iterator_view : private tamaas::iterator_::iterator<T>

#include <iterator.hh>

Public Types

using value_type = T

using difference_type = std::ptrdiff_t

using pointer = T*

using reference = T&

Public Functions

inline iterator_view(pointer data, std::size_t start, ptrdiff_t offset, std::vector<UInt> strides, std::vector<UInt> sizes)

Constructor.

inline iterator_view(const iterator_view &o)

inline iterator_view &operator=(const iterator_view &o)

Protected Functions

inline void computeAccessOffset()

Protected Attributes

std::vector<UInt> strides

std::vector<UInt> n

std::vector<UInt> tuple

class Kato : public tamaas::ContactSolver

#include <kato.hh>

Subclassed by tamaas::BeckTeboulle, tamaas::Condat, tamaas::PolonskyKeerTan

Public Functions

Kato(Model &model, const GridBase<Real> &surface, Real tolerance, Real mu)

Constructor.

virtual Real solve(std::vector<Real> p0) override

Solve.

Real solveRelaxed(GridBase<Real> &g0)

Solve relaxed problem.

Real solveRegularized(GridBase<Real> &p0, Real r)

Solve regularized problem.

Real computeCost(bool use_tresca = false)

Compute cost function.

Compute mean of the field taking each component separately.

template<model_type type>
Real solveTmpl(GridBase<Real> &p0, UInt proj_iter)

Template for solve function.

template<model_type type>
Real solveRelaxedTmpl(GridBase<Real> &g0)

Template for solveRelaxed function.

template<model_type type>
Real solveRegularizedTmpl(GridBase<Real> &p0, Real r)

Template for solveRegularized function.

template<model_type type>
void initSurfaceWithComponents()

Creates surfaceComp form surface.

template<UInt comp>
void computeGradient(bool use_tresca = false)

Compute gradient of functional.

template<UInt comp>
void enforcePressureConstraints(GridBase<Real> &p0, UInt proj_iter)

Project pressure on friction cone.

Projects \(\vec{p}\) on \(\mathcal{C}\) and \(\mathcal{D}\). Projects \(\vec{p}\) on \(\mathcal{C}\) and \(\mathcal{D}\).

template<UInt comp>
void enforcePressureMean(GridBase<Real> &p0)

Project on C.

template<UInt comp>
void enforcePressureCoulomb()

Project on D.

template<UInt comp>
void enforcePressureTresca()

Project on D (Tresca)

template<UInt comp>
Vector<Real, comp> computeMean(GridBase<Real> &field)

Comupte mean value of field.

Compute mean of the field taking each component separately.

template<UInt comp>
void addUniform(GridBase<Real> &field, GridBase<Real> &vec)

Add vector to each point of field.

template<model_type type>
void computeValuesForCost(GridBase<Real> &lambda, GridBase<Real> &eta, GridBase<Real> &p_N, GridBase<Real> &p_C)

Compute grids of dual and primal variables.

template<model_type type>
void computeValuesForCostTresca(GridBase<Real> &lambda, GridBase<Real> &eta, GridBase<Real> &p_N, GridBase<Real> &p_C)

Compute dual and primal variables with Tresca friction.

template<UInt comp>
void computeFinalGap()

Compute total displacement.

inline void setProjectionIterations(UInt niter)

Public Static Functions

static Real regularize(Real x, Real r)

Regularization function with factor r (0 -> unregugularized)

Protected Attributes

BEEngine &engine

GridBase<Real> *gap = nullptr

GridBase<Real> *pressure = nullptr

std::unique_ptr<GridBase<Real>> surfaceComp = nullptr

Real mu = 0

UInt N = 0

UInt proj_iter = 50

class KatoSaturated : public tamaas::PolonskyKeerRey

#include <kato_saturated.hh>

Polonsky-Keer algorithm with saturation of the pressure.

Public Functions

KatoSaturated(Model &model, const GridBase<Real> &surface, Real tolerance, Real pmax)

Constructor.

~KatoSaturated() override = default

virtual Real solve(std::vector<Real> load) override

Solve.

virtual Real meanOnUnsaturated(const GridBase<Real> &field) const override

Mean on unsaturated constraint zone.

virtual Real computeSquaredNorm(const GridBase<Real> &field) const override

Compute squared norm.

virtual void updateSearchDirection(Real factor) override

Update search direction.

virtual Real computeCriticalStep(Real target = 0) override

Compute critical step.

virtual bool updatePrimal(Real step) override

Update primal and check non-admissible state.

virtual Real computeError() const override

Compute error/stopping criterion.

virtual void enforceMeanValue(Real mean) override

Enfore mean value constraint.

virtual void enforceAdmissibleState() override

Enforce contact constraints on final state.

inline Real getPMax() const

Access to pmax.

inline void setPMax(Real p)

Set pax.

Protected Attributes

Real pmax = std::numeric_limits<Real>::max()

saturation pressure

template<UInt dim, UInt derivative_order>
class Kelvin

#include <influence.hh>

Class for the Kelvin tensor.

template<model_type type, UInt derivative>
class Kelvin : public tamaas::VolumePotential<type>

#include <kelvin.hh>

Kelvin tensor.

Subclassed by tamaas::Mindlin< type, derivative >

Public Functions

Kelvin(Model *model)

Constructor.

void applyIf(GridBase<Real> &source, GridBase<Real> &out, filter_t pred) const override

Apply the Kelvin-tensor_order operator.

void setIntegrationMethod(integration_method method, Real cutoff)

Set the integration method for volume operator.

virtual std::pair<UInt, UInt> matvecShape() const override

Dense shape (for Scipy integration)

virtual GridBase<Real> matvec(GridBase<Real> &X) const override

matvec definition

Protected Types

using KelvinInfluence = influence::Kelvin<trait::dimension, derivative>

using ktrait = detail::KelvinTrait<KelvinInfluence>

using Source = typename ktrait::source_t

using Out = typename ktrait::out_t

using filter_t = typename parent::filter_t

Protected Attributes

integration_method method = integration_method::linear

Real cutoff

Private Types

using trait = model_type_traits<type>

using dtrait = derivative_traits<derivative>

using parent = VolumePotential<type>

Private Functions

void linearIntegral(GridBase<Real> &out, KelvinInfluence &kelvin) const

void cutoffIntegral(GridBase<Real> &out, KelvinInfluence &kelvin) const

template<>
class Kelvin<3, 0>

#include <influence.hh>

Kelvin base tensor See arXiv:1811.11558 for details.

Subclassed by tamaas::influence::Kelvin< 3, 1 >

Public Functions

inline Kelvin(Real mu, Real nu)

template<bool upper, bool apply_q_power = false, typename ST>
inline Vector<Complex, dim> applyU0(const VectorProxy<const Real, dim - 1> &q, const StaticVector<Complex, ST, dim> &f) const

template<bool upper, bool apply_q_power = false, typename ST>
inline Vector<Complex, dim> applyU1(const VectorProxy<const Real, dim - 1> &q, const StaticVector<Complex, ST, dim> &f) const

Protected Attributes

const Real mu

const Real b

Protected Static Attributes

static constexpr UInt dim = 3

static constexpr UInt order = 0

template<>
class Kelvin<3, 1> : protected tamaas::influence::Kelvin<3, 0>

#include <influence.hh>

Kelvin first derivative.

Subclassed by tamaas::influence::Kelvin< 3, 2 >

Public Functions

template<bool upper, bool apply_q_power = false, typename ST>
inline Vector<Complex, dim> applyU0(const VectorProxy<const Real, dim - 1> &q, const StaticMatrix<Complex, ST, dim, dim> &f) const

template<bool upper, bool apply_q_power = false, typename ST>
inline Vector<Complex, dim> applyU1(const VectorProxy<const Real, dim - 1> &q, const StaticMatrix<Complex, ST, dim, dim> &f) const

Protected Static Attributes

static constexpr UInt dim = parent::dim

static constexpr UInt order = parent::order + 1

Private Types

using parent = Kelvin<3, 0>

template<>
class Kelvin<3, 2> : protected tamaas::influence::Kelvin<3, 1>

#include <influence.hh>

Kelvin second derivative.

Public Functions

template<bool upper, bool apply_q_power = false, typename ST>
inline Matrix<Complex, dim, dim> applyU0(const VectorProxy<const Real, dim - 1> &q, const StaticMatrix<Complex, ST, dim, dim> &f) const

template<bool upper, bool apply_q_power = false, typename ST>
inline Matrix<Complex, dim, dim> applyU1(const VectorProxy<const Real, dim - 1> &q, const StaticMatrix<Complex, ST, dim, dim> &f) const

template<typename ST>
inline Matrix<Complex, dim, dim> applyDiscontinuityTerm(const StaticMatrix<Complex, ST, dim, dim> &f) const

Private Types

using parent = Kelvin<3, 1>

Private Static Attributes

static constexpr UInt dim = parent::dim

static constexpr UInt order = parent::order + 1

template<model_type type, typename kelvin_t, typename = typename KelvinTrait<kelvin_t>::source_t>
struct KelvinHelper

#include <kelvin_helper.hh>

Helper to apply integral representation on output.

Public Types

using trait = model_type_traits<type>

using BufferType = GridHermitian<Real, bdim>

using source_t = typename KelvinTrait<kelvin_t>::source_t

using out_t = typename KelvinTrait<kelvin_t>::out_t

Public Functions

virtual ~KelvinHelper() = default

inline void applyIntegral(std::vector<BufferType> &source, std::vector<BufferType> &out, const Grid<Real, bdim> &wavevectors, Real domain_size, const kelvin_t &kelvin)

Apply the regular part of Kelvin to source and sum into output.

This function performs the linear integration algorithm using the accumulator.

inline void applyIntegral(std::vector<BufferType> &source, BufferType &out, UInt layer, const Grid<Real, bdim> &wavevectors, Real domain_size, Real cutoff, const kelvin_t &kelvin)

Apply the regular part of Kelvin to source and sum into output.

This function performs the cutoff integration algorithm. Not to be confused with its overload above.

inline void applyFreeTerm(std::vector<BufferType> &source, std::vector<BufferType> &out, const kelvin_t &kelvin)

Apply free term of distribution derivative.

inline void applyFreeTerm(BufferType&, BufferType&, const kelvin_t&)

Apply free term of distribution derivative (layer)

inline void makeFundamentalGreatAgain(std::vector<BufferType> &out)

Making the output free of communist NaN.

inline void makeFundamentalGreatAgain(BufferType&)

Making the output free of communist NaN (layer)

inline void applyFreeTerm(BufferType &source, BufferType &out, const influence::Kelvin<3, 2> &kelvin)

Applying free term for double gradient of Kelvin.

Public Static Attributes

static constexpr UInt dim = trait::dimension

static constexpr UInt bdim = trait::boundary_dimension

Protected Attributes

Accumulator<type, source_t> accumulator

template<typename T>
struct KelvinTrait

#include <kelvin_helper.hh>

Trait for kelvin local types.

template<UInt dim>
struct KelvinTrait<influence::Boussinesq<dim, 0>>

#include <kelvin_helper.hh>

Public Types

using source_t = VectorProxy<Complex, dim>

using out_t = VectorProxy<Complex, dim>

template<UInt dim>
struct KelvinTrait<influence::Boussinesq<dim, 1>>

#include <kelvin_helper.hh>

Public Types

using source_t = VectorProxy<Complex, dim>

using out_t = SymMatrixProxy<Complex, dim>

template<UInt dim>
struct KelvinTrait<influence::Kelvin<dim, 0>>

#include <kelvin_helper.hh>

Public Types

using source_t = VectorProxy<Complex, dim>

using out_t = VectorProxy<Complex, dim>

template<UInt dim>
struct KelvinTrait<influence::Kelvin<dim, 1>>

#include <kelvin_helper.hh>

Public Types

using source_t = SymMatrixProxy<Complex, dim>

using out_t = VectorProxy<Complex, dim>

template<UInt dim>
struct KelvinTrait<influence::Kelvin<dim, 2>>

#include <kelvin_helper.hh>

Public Types

using source_t = SymMatrixProxy<Complex, dim>

using out_t = SymMatrixProxy<Complex, dim>

class LinearElastic : public tamaas::Material

#include <linear_elastic.hh>

Public Functions

LinearElastic(Model *model, std::string operator_name)

virtual void computeStress(Field &stress, const Field &strain, const Field &strain_increment) override

Compute the stress from total strain and strain increment.

virtual void computeEigenStress(Field &stress, const Field &strain, const Field &strain_increment) override

Compute stress due to inelastic increment.

virtual void applyTangent(Field &output, const Field &input, const Field &strain, const Field &strain_increment) override

Applt consistent tangent.

virtual void update() override

Update internal variables.

Protected Attributes

std::string operator_name

Private Types

using parent = Material

using Field = parent::Field

using trait = model_type_traits<model_type::volume_2d>

Private Static Attributes

static constexpr UInt dim = trait::dimension

static constexpr UInt comp = trait::voigt

class Logger

#include <logger.hh>

Logging class Inspired from https://www.drdobbs.com/cpp/logging-in-c/201804215 by Petru Marginean.

Public Functions

~Logger() noexcept

Writing to stderr.

std::ostream &get(LogLevel level = LogLevel::debug)

Get stream.

inline decltype(auto) getWishLevel() const

Get wish log level.

Public Static Functions

static inline decltype(auto) getCurrentLevel()

Get current log level.

static void setLevel(LogLevel level)

Set acceptable logging level.

Private Members

std::ostringstream stream

LogLevel wish_level = LogLevel::debug

Private Static Attributes

static LogLevel current_level = LogLevel::info

class Loop

#include <loop.hh>

Singleton class for automated loops using lambdas.

This class is sweet candy :) It provides abstraction of the paralelism paradigm used in loops and allows simple and less error-prone loop syntax, with minimum boiler plate. I love it <3

Public Functions

Loop() = delete

Constructor.

Public Static Functions

template<typename T>
static inline arange<T> range(T size)

template<typename T, typename U>
static inline arange<T> range(U start, T size)

template<typename Functor, typename ...Ranges>
static inline auto loop(Functor &&func, Ranges&&... ranges) -> typename std::enable_if<not is_policy<Functor>::value, void>::type

Loop functor over ranges.

template<typename DerivedPolicy, typename Functor, typename ...Ranges>
static inline void loop(const thrust::execution_policy<DerivedPolicy> &policy, Functor &&func, Ranges&&... ranges)

Loop over ranges with non-default policy.

template<operation op = operation::plus, typename Functor, typename ...Ranges>
static inline auto reduce(Functor &&func, Ranges&&... ranges) -> typename std::enable_if<not is_policy<Functor>::value, decltype(func(std::declval<reference_type<Ranges>>()...))>::type

Reduce functor over ranges.

template<operation op = operation::plus, typename DerivedPolicy, typename Functor, typename ...Ranges>
static inline auto reduce(const thrust::execution_policy<DerivedPolicy> &policy, Functor &&func, Ranges&&... ranges) -> decltype(func(std::declval<reference_type<Ranges>>()...))

Reduce over ranges with non-default policy.

Private Types

template<typename T>
using reference_type = typename std::decay<T>::type::reference

Private Static Functions

template<typename DerivedPolicy, typename Functor, typename ...Ranges>
static void loopImpl(const thrust::execution_policy<DerivedPolicy> &policy, Functor &&func, Ranges&&... ranges)

Loop over ranges and apply functor.

template<operation op, typename DerivedPolicy, typename Functor, typename ...Ranges>
static auto reduceImpl(const thrust::execution_policy<DerivedPolicy> &policy, Functor &&func, Ranges&&... ranges) -> decltype(func(std::declval<reference_type<Ranges>>()...))

Loop over ranges, apply functor and reduce result.

class Material

#include <material.hh>

Subclassed by tamaas::IsotropicHardening, tamaas::LinearElastic

Public Functions

inline Material(Model *model)

Constructor.

virtual ~Material() = default

Destructor.

virtual void computeStress(Field &stress, const Field &strain, const Field &strain_increment) = 0

Compute the stress from total strain and strain increment.

virtual void computeEigenStress(Field &stress, const Field &strain, const Field &strain_increment) = 0

Compute stress due to inelastic increment.

virtual void update() = 0

Update internal variables.

inline virtual void applyTangent(Field&, const Field&, const Field&, const Field&)

Applt consistent tangent.

Protected Types

using Field = GridBase<Real>

Protected Attributes

Model *model

class MaugisAdhesionFunctional : public tamaas::functional::AdhesionFunctional

#include <adhesion_functional.hh>

Constant adhesion functional.

Public Functions

inline MaugisAdhesionFunctional(const GridBase<Real> &surface)

Explicit declaration of constructor for swig.

virtual Real computeF(GridBase<Real> &gap, GridBase<Real> &pressure) const override

Compute the total adhesion energy.

virtual void computeGradF(GridBase<Real> &gap, GridBase<Real> &gradient) const override

Compute the gradient of the adhesion functional.

class MetaFunctional : public tamaas::functional::Functional

#include <meta_functional.hh>

Meta functional that contains list of functionals.

Public Functions

virtual Real computeF(GridBase<Real> &variable, GridBase<Real> &dual) const override

Compute functional.

virtual void computeGradF(GridBase<Real> &variable, GridBase<Real> &gradient) const override

Compute functional gradient.

void addFunctionalTerm(std::shared_ptr<Functional> functional)

Add functional to the list.

void clear()

Clears the functional list.

Protected Attributes

FunctionalList functionals

Private Types

using FunctionalList = std::list<std::shared_ptr<Functional>>

template<model_type type, UInt derivative>
class Mindlin : public tamaas::Kelvin<type, derivative>

#include <mindlin.hh>

Mindlin tensor.

Public Functions

Mindlin(Model *model)

Constructor.

void applyIf(GridBase<Real> &source, GridBase<Real> &out, filter_t pred) const override

Apply the Mindlin-tensor_order operator.

Protected Functions

void linearIntegral(GridBase<Real> &out) const

void cutoffIntegral(GridBase<Real> &out) const

Protected Attributes

mutable GridHermitian<Real, trait::boundary_dimension> surface_tractions

Private Types

using trait = model_type_traits<type>

using parent = Kelvin<type, derivative>

using filter_t = typename parent::filter_t

class Model : public tamaas::FieldContainer

#include <model.hh>

Model containing pressure and displacement This class is a container for the model fields. It is supposed to be dimension agnostic, hence the GridBase members.

Subclassed by tamaas::ModelTemplate< type >

Public Functions

void setElasticity(Real E, Real nu)

Set elasticity parameters.

inline Real getHertzModulus() const

Get Hertz contact modulus.

inline Real getYoungModulus() const

Get Young’s modulus.

inline Real getPoissonRatio() const

Get Poisson’s ratio.

inline Real getShearModulus() const

Get shear modulus.

inline void setYoungModulus(Real E_)

Set Young’s modulus.

inline void setPoissonRatio(Real nu_)

Set Poisson’s ratio.

virtual model_type getType() const = 0

Get model type.

const std::vector<Real> &getSystemSize() const

Get system physical size.

virtual std::vector<Real> getBoundarySystemSize() const = 0

Get boundary system physical size.

const std::vector<UInt> &getDiscretization() const

Get discretization.

virtual std::vector<UInt> getGlobalDiscretization() const = 0

Get discretization of global MPI system.

virtual std::vector<UInt> getBoundaryDiscretization() const = 0

Get boundary discretization.

inline BEEngine &getBEEngine()

Get boundary element engine.

void applyElasticity(GridBase<Real> &stress, const GridBase<Real> &strain) const

Apply Hooke’s law.

void solveNeumann()

Solve Neumann problem using default neumann operator.

void solveDirichlet()

Solve Dirichlet problem using default dirichlet operator.

template<typename Operator>
std::shared_ptr<IntegralOperator> registerIntegralOperator(const std::string &name)

Register a new integral operator.

void registerIntegralOperator(const std::string &name, std::shared_ptr<IntegralOperator> op)

Register external operator.

std::shared_ptr<IntegralOperator> getIntegralOperator(const std::string &name) const

Get a registerd integral operator.

std::vector<std::string> getIntegralOperators() const

Get list of integral operators.

inline const auto &getIntegralOperatorsMap() const

Get operators mapcar.

void updateOperators()

Tell operators to update their cache.

virtual void setIntegrationMethod(integration_method method, Real cutoff) = 0

Set integration method for registered volume operators.

GridBase<Real> &getTraction()

Get pressure.

const GridBase<Real> &getTraction() const

Get pressure.

GridBase<Real> &getDisplacement()

Get displacement.

const GridBase<Real> &getDisplacement() const

Get displacement.

template<class T>
inline bool isBoundaryField(const GridBase<T> &field) const

Determine if a field is defined on boundary.

std::vector<std::string> getBoundaryFields() const

Return list of fields defined on boundary.

void addDumper(std::shared_ptr<ModelDumper> dumper)

Set the dumper object.

void dump() const

Dump the model.

Protected Functions

inline Model(std::vector<Real> system_size, std::vector<UInt> discretization)

Constructor.

Protected Attributes

Real E = 1

Real nu = 0

std::vector<Real> system_size

std::vector<UInt> discretization

std::unique_ptr<BEEngine> engine = nullptr

std::unordered_map<std::string, std::shared_ptr<IntegralOperator>> operators

std::vector<std::shared_ptr<ModelDumper>> dumpers

Friends

friend std::ostream &operator<<(std::ostream &o, const Model &_this)

class model_type_error : public domain_error

#include <errors.hh>

template<model_type type>
struct model_type_traits

#include <model_type.hh>

Trait class to store physical dimension of domain, of boundary and number of components

template<>
struct model_type_traits<model_type::basic_1d>

#include <model_type.hh>

Public Static Attributes

static constexpr char repr[] = {"basic_1d"}

static constexpr UInt dimension = 1

static constexpr UInt components = 1

static constexpr UInt boundary_dimension = 1

static constexpr UInt voigt = voigt_size<1>::value

static const std::vector<UInt> indices = {}

template<>
struct model_type_traits<model_type::basic_2d>

#include <model_type.hh>

Public Static Attributes

static constexpr char repr[] = {"basic_2d"}

static constexpr UInt dimension = 2

static constexpr UInt components = 1

static constexpr UInt boundary_dimension = 2

static constexpr UInt voigt = voigt_size<1>::value

static const std::vector<UInt> indices = {}

template<>
struct model_type_traits<model_type::surface_1d>

#include <model_type.hh>

Public Static Attributes

static constexpr char repr[] = {"surface_1d"}

static constexpr UInt dimension = 1

static constexpr UInt components = 2

static constexpr UInt boundary_dimension = 1

static constexpr UInt voigt = voigt_size<2>::value

static const std::vector<UInt> indices = {}

template<>
struct model_type_traits<model_type::surface_2d>

#include <model_type.hh>

Public Static Attributes

static constexpr char repr[] = {"surface_2d"}

static constexpr UInt dimension = 2

static constexpr UInt components = 3

static constexpr UInt boundary_dimension = 2

static constexpr UInt voigt = voigt_size<3>::value

static const std::vector<UInt> indices = {}

template<>
struct model_type_traits<model_type::volume_1d>

#include <model_type.hh>

Public Static Attributes

static constexpr char repr[] = {"volume_1d"}

static constexpr UInt dimension = 2

static constexpr UInt components = 2

static constexpr UInt boundary_dimension = 1

static constexpr UInt voigt = voigt_size<2>::value

static const std::vector<UInt> indices = {0}

template<>
struct model_type_traits<model_type::volume_2d>

#include <model_type.hh>

Public Static Attributes

static constexpr char repr[] = {"volume_2d"}

static constexpr UInt dimension = 3

static constexpr UInt components = 3

static constexpr UInt boundary_dimension = 2

static constexpr UInt voigt = voigt_size<3>::value

static const std::vector<UInt> indices = {0}

class ModelDumper

#include <model_dumper.hh>

Public Functions

virtual ~ModelDumper() = default

virtual void dump(const Model &model) = 0

class ModelFactory

#include <model_factory.hh>

Factory class for model.

Public Static Functions

static std::unique_ptr<Model> createModel(model_type type, const std::vector<Real> &system_size, const std::vector<UInt> &discretization)

Create new model.

static std::unique_ptr<Model> createModel(const Model &model)

Make a deep copy of existing model.

static std::unique_ptr<Residual> createResidual(Model &model, Real sigma_y, Real hardening)

Create a plasticity residual.

static void registerVolumeOperators(Model &m)

Register volume integral operators in a model.

static void registerNonPeriodic(Model &m, std::string name)

static void setIntegrationMethod(IntegralOperator &op, integration_method method, Real cutoff)

Set integration method for a volume integral operator.

template<model_type type>
class ModelTemplate : public tamaas::Model

#include <model_template.hh>

Model class templated with model type Specializations of this class should take care of dimension specific code.

Public Functions

ModelTemplate(std::vector<Real> system_size, std::vector<UInt> discretization)

Constructor.

inline virtual model_type getType() const override

Get model type.

virtual std::vector<UInt> getGlobalDiscretization() const override

Get discretization of global MPI system.

virtual std::vector<UInt> getBoundaryDiscretization() const override

Get boundary discretization.

virtual std::vector<Real> getBoundarySystemSize() const override

Get boundary system physical size.

virtual void setIntegrationMethod(integration_method method, Real cutoff) override

Set integration method for registered volume operators.

Protected Functions

void initializeBEEngine()

Protected Attributes

std::unique_ptr<ViewType> displacement_view = nullptr

std::unique_ptr<ViewType> traction_view = nullptr

Private Types

using trait = model_type_traits<type>

using ViewType = GridView<Grid, Real, dim, trait::boundary_dimension>

Private Static Attributes

static constexpr UInt dim = trait::dimension

struct MPI_Comm

#include <mpi_interface.hh>

class nan_error : public runtime_error

#include <errors.hh>

struct no_convergence_error : public runtime_error

#include <errors.hh>

Public Functions

inline no_convergence_error(const std::string &what, double error, double tolerance)

inline const char *what() const noexcept override

Public Members

double error

double tolerance

class not_implemented_error : public runtime_error

#include <errors.hh>

template<UInt dim>
struct Partitioner

#include <partitioner.hh>

Public Static Functions

template<typename Container>
static inline decltype(auto) global_size(Container local)

template<typename T>
static inline decltype(auto) global_size(const Grid<T, dim> &grid)

template<typename Container>
static inline decltype(auto) local_size(Container global)

template<typename T>
static inline decltype(auto) local_size(const Grid<T, dim> &grid)

static inline decltype(auto) local_size(std::initializer_list<UInt> list)

template<typename Container>
static inline decltype(auto) local_offset(const Container &global)

template<typename T>
static inline decltype(auto) local_offset(const Grid<T, dim> &grid)

static inline decltype(auto) local_offset(std::initializer_list<UInt> list)

template<typename Container>
static inline decltype(auto) cast_size(const Container &s)

static inline decltype(auto) alloc_size(const std::array<UInt, dim> &global, UInt howmany)

template<typename T>
static inline Grid<T, dim> gather(const Grid<T, dim> &send)

template<typename T>
static inline Grid<T, dim> scatter(const Grid<T, dim> &send)

class PETScSolver : public tamaas::EPSolver

#include <petsc_solver.hh>

Wrapper to PETSc SNES abstract solver.

Public Types

using residual_ctx = std::pair<Residual*, GridBase<Real>*>

Public Functions

PETScSolver(Residual &residual, std::string petsc_args)

~PETScSolver() override

virtual void solve() override

Private Members

PetscOptions snes_options

Vec _xvec

Vec _rvec

Mat J

SNES snes

residual_ctx res_ctx

struct plan

#include <cufft_engine.hh>

Public Functions

plan() = default

inline plan(plan &&o) noexcept

inline plan &operator=(plan &&o) noexcept

inline ~plan() noexcept

Destroy plan.

inline operator cufftHandle() const

For seamless use with fftw api.

Public Members

cufftHandle _plan

template<typename T>
struct plan

#include <interface_impl.hh>

Holder type for fftw plans.

Public Functions

inline explicit plan(typename helper<T>::plan _plan = nullptr)

Create from plan.

inline plan(plan &&o) noexcept

Move constructor to avoid accidental plan destruction.

inline plan &operator=(plan &&o) noexcept

Move operator.

inline ~plan() noexcept

Destroy plan.

inline operator typename helper<T>::plan() const

For seamless use with fftw api.

Public Members

helper<T>::plan _plan

class PolonskyKeerRey : public tamaas::ContactSolver

#include <polonsky_keer_rey.hh>

Subclassed by tamaas::KatoSaturated

Public Types

enum type

Types of algorithm (primal/dual) or constraint.

Values:

enumerator gap

enumerator pressure

Public Functions

PolonskyKeerRey(Model &model, const GridBase<Real> &surface, Real tolerance, type variable_type, type constraint_type)

Constructor.

~PolonskyKeerRey() override = default

virtual Real solve(std::vector<Real> target) override

Solve.

virtual Real meanOnUnsaturated(const GridBase<Real> &field) const

Mean on unsaturated constraint zone.

Computes \( \frac{1}{\mathrm{card}(\{p > 0\})} \sum_{\{p > 0\}}{f_i} \)

virtual Real computeSquaredNorm(const GridBase<Real> &field) const

Compute squared norm.

Computes \( \sum_{\{p > 0\}}{f_i^2} \)

virtual void updateSearchDirection(Real factor)

Update search direction.

Do \(\mathbf{t} = \mathbf{q}' + \delta \frac{R}{R_\mathrm{old}}\mathbf{t} \)

virtual Real computeCriticalStep(Real target = 0)

Compute critical step.

Computes \( \tau = \frac{ \sum_{\{p > 0\}}{q_i't_i} }{ \sum_{\{p > 0\}}{r_i' t_i} } \)

virtual bool updatePrimal(Real step)

Update primal and check non-admissible state.

Update steps:

1. \(\mathbf{p} = \mathbf{p} - \tau \mathbf{t} \)

2. Truncate all \(p\) negative

3. For all points in \(I_\mathrm{na} = \{p = 0 \land q < 0 \}\) do \(p_i = p_i - \tau q_i\)

virtual Real computeError() const

Compute error/stopping criterion.

Error is based on \( \sum{p_i q_i} \)

virtual void enforceAdmissibleState()

Enforce contact constraints on final state.

virtual void enforceMeanValue(Real mean)

Enfore mean value constraint.

void setIntegralOperator(std::string name)

Set integral operator for gradient computation.

void setupFunctional()

Set functionals for contact.

Protected Attributes

type variable_type

type constraint_type

model_type operation_type

GridBase<Real> *primal = nullptr

non-owning pointer for primal varaible

GridBase<Real> *dual = nullptr

non-owning pointer for dual variable

std::unique_ptr<GridBase<Real>> search_direction = nullptr

CG search direction.

std::unique_ptr<GridBase<Real>> projected_search_direction = nullptr

Projected CG search direction.

std::unique_ptr<GridBase<Real>> pressure_view

View on normal pressure, gap, displacement.

std::unique_ptr<GridBase<Real>> gap_view

std::unique_ptr<GridBase<Real>> displacement_view = nullptr

std::shared_ptr<IntegralOperator> integral_op = nullptr

Integral operator for gradient computation.

Private Functions

template<model_type type>
void setViews()

Set correct views on normal traction and gap.

template<model_type type>
void defaultOperator()

Set the default integral operator.

class PolonskyKeerTan : public tamaas::Kato

#include <polonsky_keer_tan.hh>

Public Functions

PolonskyKeerTan(Model &model, const GridBase<Real> &surface, Real tolerance, Real mu)

Constructor.

virtual Real solve(std::vector<Real> p0) override

Solve with Coulomb friction.

Real solveTresca(GridBase<Real> &p0)

Solve with Tresca friction.

template<model_type type>
Real solveTmpl(GridBase<Real> &p0, bool use_tresca = false)

Template for solve function.

template<UInt comp>
void enforcePressureMean(GridBase<Real> &p0)

Enforce pressure mean.

template<UInt comp>
Vector<Real, comp> computeMean(GridBase<Real> &field, bool on_c)

Compute mean of field (only on I_c)

Real computeSquaredNorm(GridBase<Real> &field)

Compute squared norm.

template<UInt comp>
void truncateSearchDirection(bool on_c)

Restrict search direction on I_c.

template<UInt comp>
Real computeStepSize(bool on_c)

Compute optimal step size (only on I_c)

Private Members

std::unique_ptr<GridBase<Real>> search_direction = nullptr

std::unique_ptr<GridBase<Real>> search_direction_backup = nullptr

std::unique_ptr<GridBase<Real>> projected_search_direction = nullptr

template<UInt... ns>
struct product : public detail::product_tail_rec<1, ns...>

#include <static_types.hh>

template<UInt acc, UInt n>
struct product_tail_rec<acc, n> : public std::integral_constant<UInt, acc * n>

#include <static_types.hh>

template<typename T>
struct ptr

#include <interface_impl.hh>

RAII helper for fftw_free.

Public Functions

inline ~ptr() noexcept

inline operator T*()

Public Members

T *_ptr

template<typename LocalType, typename ValueType, UInt local_size>
class Range

#include <ranges.hh>

Range class for complex iterators.

Public Types

using value_type = LocalType

using reference = value_type&&

Public Functions

template<class Container>
inline Range(Container &&cont)

Construct from a container.

inline Range(iterator _begin, iterator _end)

Construct from two iterators.

inline iterator begin()

inline iterator end()

inline Range headless() const

Private Members

iterator _begin

iterator _end

template<operation op, typename ReturnType>
struct reduction_helper

#include <loop_utils.hh>

template<typename ReturnType>
struct reduction_helper<operation::max, ReturnType> : public thrust::maximum<ReturnType>

#include <loop_utils.hh>

Public Functions

inline ReturnType init() const

template<typename ReturnType>
struct reduction_helper<operation::min, ReturnType> : public thrust::minimum<ReturnType>

#include <loop_utils.hh>

Public Functions

inline ReturnType init() const

template<typename ReturnType>
struct reduction_helper<operation::plus, ReturnType> : public thrust::plus<ReturnType>

#include <loop_utils.hh>

Public Functions

inline ReturnType init() const

template<typename ReturnType>
struct reduction_helper<operation::times, ReturnType> : public thrust::multiplies<ReturnType>

#include <loop_utils.hh>

Public Functions

inline ReturnType init() const

template<UInt dim>
class RegularizedPowerlaw : public tamaas::Filter<dim>

#include <regularized_powerlaw.hh>

Class representing an isotropic power law spectrum.

Public Functions

virtual void computeFilter(GridHermitian<Real, dim> &filter_coefficients) const override

Compute filter coefficients.

inline Real operator()(const VectorProxy<Real, dim> &q_vec) const

Compute a point of the PSD.

TAMAAS_ACCESSOR(q1, UInt, Q1)

TAMAAS_ACCESSOR(q2, UInt, Q2)

TAMAAS_ACCESSOR(hurst, Real, Hurst)

Protected Attributes

UInt q1

UInt q2

Real hurst

class Residual

#include <residual.hh>

Residual manager.

Public Functions

Residual(Model &model, std::shared_ptr<Material> material)

Constructor.

virtual ~Residual() = default

Destructor.

virtual void computeResidual(GridBase<Real> &strain_increment)

Compute the residual vector for a given strain increment.

virtual void computeResidualDisplacement(GridBase<Real> &strain_increment)

Compute residual surface displacement.

virtual void applyTangent(GridBase<Real> &output, GridBase<Real> &input, GridBase<Real> &strain_increment)

Apply tangent to arbitrary increment.

virtual void updateState(GridBase<Real> &converged_strain_increment)

Update the plastic state.

inline const Model &getModel() const

Return model reference.

inline Model &getModel()

Return model reference (non-const)

inline const GridBase<Real> &getVector() const

Return residual vector.

inline const Material &getMaterial() const

Return material.

Protected Attributes

Model &model

std::shared_ptr<Material> material

std::shared_ptr<Grid<Real, 3>> strain

std::shared_ptr<Grid<Real, 3>> stress

std::shared_ptr<Grid<Real, 3>> residual

std::shared_ptr<Grid<Real, 3>> tmp

std::unordered_set<UInt> plastic_layers

std::function<bool(UInt)> plastic_filter

Private Functions

inline const IntegralOperator &integralOperator(const std::string &name) const

Convenience function.

void updateFilter(Grid<Real, dim> &plastic_strain_increment)

Add non-zero layers of plastic strain into the filter.

Private Static Attributes

static constexpr auto type = model_type::volume_2d

static constexpr auto dim = model_type_traits<type>::dimension

static constexpr auto voigt = model_type_traits<type>::voigt

struct sequential

#include <mpi_interface.hh>

Public Static Functions

static inline void enter()

static inline void exit()

struct sequential_guard

#include <mpi_interface.hh>

Public Functions

inline sequential_guard()

inline ~sequential_guard()

template<typename T>
struct span

#include <span.hh>

Public Types

using element_type = T

using value_type = std::remove_cv_t<T>

using size_type = std::size_t

using difference_type = std::ptrdiff_t

using pointer = T*

using const_pointer = const T*

using reference = T&

using const_reference = const T&

using iterator = T*

using reverse_iterator = std::reverse_iterator<iterator>

Public Functions

inline constexpr size_type size() const noexcept

inline constexpr pointer data() const noexcept

inline constexpr iterator begin() const noexcept

inline constexpr iterator end() const noexcept

inline constexpr iterator begin() noexcept

inline constexpr iterator end() noexcept

inline reference operator[](size_type idx)

inline const_reference operator[](size_type idx) const

Public Members

pointer data_ = nullptr

size_type size_ = 0

class SquaredExponentialAdhesionFunctional : public tamaas::functional::AdhesionFunctional

#include <adhesion_functional.hh>

Squared exponential adhesion functional.

Public Functions

inline SquaredExponentialAdhesionFunctional(const GridBase<Real> &surface)

Explicit declaration of constructor for swig.

virtual Real computeF(GridBase<Real> &gap, GridBase<Real> &pressure) const override

Compute the total adhesion energy.

virtual void computeGradF(GridBase<Real> &gap, GridBase<Real> &gradient) const override

Compute the gradient of the adhesion functional.

template<template<typename, typename, UInt...> class StaticParent, UInt... dims>
struct static_size_helper : public tamaas::product<dims...>

#include <static_types.hh>

template<UInt n>
struct static_size_helper<StaticSymMatrix, n> : public tamaas::voigt_size<n>

#include <static_types.hh>

template<typename DataType, typename SupportType, UInt _size>
class StaticArray

#include <static_types.hh>

Static Array.

This class is meant to be a small and fast object for intermediate calculations, possibly on wrapped memory belonging to a grid. Support type show be either a pointer or a C array. It should not contain any virtual method.

Public Types

using value_type = T

Public Functions

StaticArray() = default

~StaticArray() = default

StaticArray(const StaticArray&) = delete

StaticArray(StaticArray&&) = delete

StaticArray &operator=(StaticArray&&) = delete

inline auto operator()(UInt i) -> T&

Access operator.

inline auto operator()(UInt i) const -> const T&

Access operator.

template<typename DT, typename ST>
inline auto dot(const StaticArray<DT, ST, size> &o) const -> T_bare

Scalar product.

inline T_bare l2squared() const

L2 norm squared.

inline T_bare l2norm() const

L2 norm.

inline T_bare sum() const

Sum of all elements.

template<typename DT, typename ST> inline __host__ void operator+= (const StaticArray< DT, ST, size > &o)

template<typename DT, typename ST> inline __host__ void operator-= (const StaticArray< DT, ST, size > &o)

template<typename DT, typename ST> inline __host__ void operator*= (const StaticArray< DT, ST, size > &o)

template<typename DT, typename ST> inline __host__ void operator/= (const StaticArray< DT, ST, size > &o)

template<typename T1> inline __host__ std::enable_if_t< is_arithmetic< T1 >::value, StaticArray & > operator+= (const T1 &x)

template<typename T1> inline __host__ std::enable_if_t< is_arithmetic< T1 >::value, StaticArray & > operator-= (const T1 &x)

template<typename T1> inline __host__ std::enable_if_t< is_arithmetic< T1 >::value, StaticArray & > operator*= (const T1 &x)

template<typename T1> inline __host__ std::enable_if_t< is_arithmetic< T1 >::value, StaticArray & > operator/= (const T1 &x)

template<typename T1> inline __host__ std::enable_if_t< is_arithmetic< T1 >::value, StaticArray & > operator= (const T1 &x)

inline StaticArray &operator=(const StaticArray &o)

Overriding the implicit copy operator.

template<typename DT, typename ST>
inline void operator=(const StaticArray<DT, ST, size> &o)

template<typename DT, typename ST>
inline StaticArray &copy(const StaticArray<DT, ST, size> &o)

inline T *begin()

inline const T *begin() const

inline T *end()

inline const T *end() const

inline valid_size_t<T&> front()

inline valid_size_t<const T&> front() const

inline valid_size_t<T&> back()

inline valid_size_t<const T&> back() const

Public Static Attributes

static constexpr UInt size = _size

Protected Attributes

SupportType _mem

Private Types

using T = DataType

using T_bare = typename std::remove_cv_t<T>

template<typename U>
using valid_size_t = std::enable_if_t<(size > 0), U>

template<typename DataType, typename SupportType, UInt n, UInt m>
class StaticMatrix : public tamaas::StaticTensor<DataType, SupportType, n, m>

#include <static_types.hh>

Public Functions

template<typename DT, typename ST>
std::enable_if_t<n == m> fromSymmetric(const StaticSymMatrix<DT, ST, n> &o)

template<typename DT1, typename ST1, typename DT2, typename ST2>
void outer(const StaticVector<DT1, ST1, n> &a, const StaticVector<DT2, ST2, m> &b)

Outer product of two vectors.

template<typename DT1, typename ST1, typename DT2, typename ST2, UInt l>
inline void mul(const StaticMatrix<DT1, ST1, n, l> &a, const StaticMatrix<DT2, ST2, l, m> &b)

inline std::enable_if_t<n == m, T_bare> trace() const

template<typename DT1, typename ST1>
inline std::enable_if_t<n == m> deviatoric(const StaticMatrix<DT1, ST1, n, m> &mat, Real factor = n)

Private Types

using T = DataType

using T_bare = typename std::remove_cv_t<T>

template<typename DataType, typename SupportType, UInt n>
class StaticSymMatrix

#include <static_types.hh>

Symmetric matrix in Voigt notation.

Public Functions

template<typename DT, typename ST>
inline void symmetrize(const StaticMatrix<DT, ST, n, n> &m)

Copy values from matrix and symmetrize.

template<typename DT, typename ST>
inline void operator+=(const StaticMatrix<DT, ST, n, n> &m)

Add values from symmetrized matrix.

inline auto trace() const

template<typename DT, typename ST>
inline void deviatoric(const StaticSymMatrix<DT, ST, n> &m, Real factor = n)

Private Types

using parent = StaticVector<DataType, SupportType, voigt_size<n>::value>

using T = std::remove_cv_t<DataType>

Private Functions

template<typename DT, typename ST, typename BinOp>
inline void sym_binary(const StaticMatrix<DT, ST, n, n> &m, BinOp &&op)

template<typename DataType, typename SupportType = DataType*, UInt... dims>
class StaticTensor : public tamaas::StaticArray<DataType, DataType*, product<dims...>::value>

#include <static_types.hh>

Static Tensor.

This class implements a multi-dimensional tensor behavior.

Public Functions

template<typename ...Idx>
inline const T &operator()(Idx... idx) const

template<typename ...Idx>
inline T &operator()(Idx... idx)

Public Static Attributes

static constexpr UInt dim = sizeof...(dims)

Private Types

using parent = StaticArray<DataType, SupportType, product<dims...>::value>

using T = DataType

Private Static Functions

template<typename ...Idx>
static inline UInt unpackOffset(UInt offset, UInt index, Idx... rest)

template<typename ...Idx>
static inline UInt unpackOffset(UInt offset, UInt index)

template<typename DataType, typename SupportType, UInt n>
class StaticVector

#include <static_types.hh>

Vector class with size determined at compile-time.

Public Functions

template<bool transpose, typename DT1, typename ST1, typename DT2, typename ST2, UInt m>
inline void mul(const StaticMatrix<DT1, ST1, n, m> &mat, const StaticVector<DT2, ST2, m> &vec)

Matrix-vector product.

Private Types

using T = std::remove_cv_t<DataType>

template<UInt dim>
struct Statistics

#include <statistics.hh>

Suitcase class for all statistics related functions.

Public Types

using PVector = VectorProxy<Real, dim>

Public Functions

std::vector<Real> computeMoments(Grid<Real, 1> &surface)

std::vector<Real> computeMoments(Grid<Real, 2> &surface)

Public Static Functions

static Real computeRMSHeights(Grid<Real, dim> &surface)

Compute hrms.

static Real computeSpectralRMSSlope(Grid<Real, dim> &surface)

Compute hrms’ in fourier space.

static Real computeFDRMSSlope(Grid<Real, dim> &surface)

Compute hrms’ with finite differences.

static GridHermitian<Real, dim> computePowerSpectrum(Grid<Real, dim> &surface)

Compute PSD of surface.

static Grid<Real, dim> computeAutocorrelation(Grid<Real, dim> &surface)

Compute autocorrelation.

static std::vector<Real> computeMoments(Grid<Real, dim> &surface)

Compute spectral moments.

static Real contact(const Grid<Real, dim> &tractions, UInt perimeter = 0)

Compute (corrected) contact area fraction.

static Real graphArea(const Grid<Real, dim> &displacement)

Compute the area scaling factor of a periodic graph.

Private Static Functions

template<class T>
static Real rmsSlopesFromPSD(const GridHermitian<Real, dim> &psd, const Grid<T, dim> &diff)

template<UInt dim>
class SurfaceGenerator

#include <surface_generator.hh>

Class generating random surfaces.

Subclassed by tamaas::SurfaceGeneratorFilter< dim >

Public Functions

SurfaceGenerator() = default

Default constructor.

inline SurfaceGenerator(std::array<UInt, dim> global_size)

Construct with surface global size.

virtual ~SurfaceGenerator() = default

Default destructor.

virtual Grid<Real, dim> &buildSurface() = 0

Build surface profile (array of heights)

void setSizes(std::array<UInt, dim> n)

Set surface sizes.

void setSizes(const UInt n[dim])

Set surface sizes.

inline auto getSizes() const

Get surface sizes.

inline long getRandomSeed() const

void setRandomSeed(long seed)

Protected Attributes

Grid<Real, dim> grid

std::array<UInt, dim> global_size = {0}

long random_seed = 0

template<UInt dim>
class SurfaceGeneratorFilter : public tamaas::SurfaceGenerator<dim>

#include <surface_generator_filter.hh>

Subclassed by tamaas::SurfaceGeneratorRandomPhase< dim >

Public Functions

virtual Grid<Real, dim> &buildSurface() override

Construct with surface size.

Build surface with Hu & Tonder algorithm

inline void setFilter(std::shared_ptr<Filter<dim>> new_filter)

Set filter object.

inline void setSpectrum(std::shared_ptr<Filter<dim>> spectrum)

Set spectrum.

inline const Filter<dim> *getSpectrum() const

Get spectrum.

Protected Functions

void applyFilterOnSource()

Apply filter coefficients on white noise.

template<typename T>
void generateWhiteNoise()

Generate white noise with given distribution.

Protected Attributes

std::shared_ptr<Filter<dim>> filter = nullptr

GridHermitian<Real, dim> filter_coefficients

Grid<Real, dim> white_noise

std::unique_ptr<FFTEngine> engine = FFTEngine::makeEngine()

template<UInt dim>
class SurfaceGeneratorRandomPhase : public tamaas::SurfaceGeneratorFilter<dim>

#include <surface_generator_random_phase.hh>

Public Functions

virtual Grid<Real, dim> &buildSurface() override

Build surface with uniform random phase.

template<model_type type>
struct SurfaceTractionHelper

#include <kelvin_helper.hh>

Public Types

using trait = model_type_traits<type>

using BufferType = GridHermitian<Real, bdim>

using kelvin_t = influence::Kelvin<3, 2>

using source_t = typename KelvinTrait<kelvin_t>::source_t

using out_t = typename KelvinTrait<kelvin_t>::out_t

Public Functions

template<bool apply_q_power>
inline void computeSurfaceTractions(std::vector<BufferType> &source, BufferType &tractions, const Grid<Real, bdim> &wavevectors, Real domain_size, const kelvin_t &kelvin, const influence::ElasticHelper<dim> &el)

Compute surface tractions due to eigenstress distribution.

Public Static Attributes

static constexpr UInt dim = trait::dimension

static constexpr UInt bdim = trait::boundary_dimension

Protected Attributes

Accumulator<type, source_t> accumulator

template<UInt dim>
struct SymHookeFieldHelper

Public Functions

inline void operator()(SymMatrixProxy<Real, dim> sigma, SymMatrixProxy<const Real, dim> epsilon, const Real &mu, const Real &nu)

Public Members

influence::ElasticHelper<dim> elasticity = {0, 0}

struct TamaasInfo

#include <tamaas_info.hh>

Public Static Attributes

static const std::string version

static const std::string build_type

static const std::string branch

static const std::string commit

static const std::string remotes

static const std::string diff

static const std::string backend

static const bool has_mpi

static const bool has_petsc

template<template<typename, typename, UInt...> class StaticParent, typename T, UInt... dims>
class Tensor : public StaticParent<T, T[static_size_helper<StaticParent, dims...>::value], dims...>

#include <static_types.hh>

Public Functions

Tensor() = default

Default constructor.

inline Tensor(T val)

Construct with default value.

inline Tensor(const std::array<T, size> &arr)

Construct from array.

inline Tensor &operator=(const std::array<T, size> &arr)

Copy from array.

template<typename DT, typename ST>
inline Tensor(const StaticParent<DT, ST, dims...> &o)

Construct by copy from static tensor.

inline Tensor(const Tensor &o)

inline Tensor &operator=(const Tensor &o)

inline Tensor(Tensor &&o) noexcept

Private Types

using parent = StaticParent<T, T[size], dims...>

Private Static Attributes

static constexpr UInt size = static_size_helper<StaticParent, dims...>::value

template<template<typename, typename, UInt...> class StaticParent, typename T, UInt... dims>
class TensorProxy : public StaticParent<T, T*, dims...>

#include <static_types.hh>

Proxy type for tensor.

Public Types

using stack_type = Tensor<StaticParent, T, dims...>

Public Functions

inline explicit TensorProxy(T *spot)

Explicit construction from data location.

inline explicit TensorProxy(T &spot)

Explicit construction from lvalue-reference.

template<typename DataType, typename SupportType>
inline TensorProxy(StaticParent<DataType, SupportType, dims...> &o)

Construction from static tensor.

inline TensorProxy(const TensorProxy &o)

inline TensorProxy &operator=(const TensorProxy &o)

inline TensorProxy(TensorProxy &&o) noexcept

Private Types

using parent = StaticParent<T, T*, dims...>

struct ToleranceManager

#include <ep_solver.hh>

Public Functions

inline ToleranceManager(Real start, Real end, Real rate)

inline void step()

inline void reset()

Public Members

Real start_tol

Real end_tol

Real rate

Real tolerance

template<typename Iterator, typename Functor, typename Value>
class transform_iterator : public thrust::iterator_adaptor<transform_iterator<Iterator, Functor, Value>, Iterator, Value, thrust::use_default, thrust::use_default, Value>

#include <loop.hh>

Replacement for thrust::transform_iterator which copies values.

Public Types

using super_t = thrust::iterator_adaptor<transform_iterator<Iterator, Functor, Value>, Iterator, Value, thrust::use_default, thrust::use_default, Value>

Public Functions

inline transform_iterator(const Iterator &x, const Functor &func)

Private Functions

inline auto dereference() const -> decltype(func(*this->base()))

Private Members

Functor func

Friends

friend class thrust::iterator_core_access

template<typename T>
struct UnifiedAllocator

#include <unified_allocator.hh>

Class allocating unified memory

Public Static Functions

static inline span<T> allocate(typename span<T>::size_type n) noexcept

Allocate memory.

static inline void deallocate(span<T> view) noexcept

Free memory.

template<UInt dim>
struct voigt_size

#include <static_types.hh>

template<>
struct voigt_size<1> : public std::integral_constant<UInt, 1>

#include <static_types.hh>

template<>
struct voigt_size<2> : public std::integral_constant<UInt, 3>

#include <static_types.hh>

template<>
struct voigt_size<3> : public std::integral_constant<UInt, 6>

#include <static_types.hh>

template<model_type type>
class VolumePotential : public tamaas::IntegralOperator

#include <volume_potential.hh>

Volume potential operator class. Applies the operators for computation of displacements and strains due to residual/eigen strains.

Subclassed by tamaas::Boussinesq< type, derivative >, tamaas::Kelvin< type, derivative >

Public Functions

VolumePotential(Model *model)

inline virtual void updateFromModel() override

Update from model (does nothing)

inline virtual IntegralOperator::kind getKind() const override

Kind.

virtual model_type getType() const override

Type.

inline virtual void apply(GridBase<Real> &input, GridBase<Real> &output) const override

Apply to all of the source layers.

Protected Types

using filter_t = const std::function<bool(UInt)>&

using BufferType = GridHermitian<Real, trait::boundary_dimension>

Protected Functions

void transformSource(GridBase<Real> &in, filter_t pred) const

Transform source layer-by-layer.

inline void transformSource(GridBase<Real> &in) const

Transform all source.

template<typename Func>
void transformOutput(Func func, GridBase<Real> &out) const

Transform output layer-by-layer.

void initialize(UInt source_components, UInt out_components, UInt out_buffer_size)

Initialize fourier buffers.

Protected Attributes

Grid<Real, trait::boundary_dimension> wavevectors

mutable std::vector<BufferType> source_buffer

mutable std::vector<BufferType> out_buffer

mutable std::unique_ptr<FFTEngine> engine

Private Types

using trait = model_type_traits<type>

struct VonMises

#include <computes.hh>

Compute von Mises stress on a tensor field.

Public Static Functions

template<UInt dim>
static inline void call(Grid<Real, dim> &vm, const Grid<Real, dim> &stress)

template<model_type mtype, IntegralOperator::kind otype>
class Westergaard : public tamaas::IntegralOperator

#include <westergaard.hh>

Operator based on Westergaard solution and the Dicrete Fourier Transform. This class is templated with model type to allow efficient storage of the influence coefficients. The integral operator is only applied to surface pressure/displacements, even for volume models.

Public Functions

Westergaard(Model *model)

Constuctor: initalizes influence coefficients and allocates buffer.

inline const GridHermitian<Real, bdim> &getInfluence() const

Get influence coefficients.

virtual void apply(GridBase<Real> &input, GridBase<Real> &output) const override

Apply influence coefficients to input.

inline virtual void updateFromModel() override

Update the influence coefficients.

inline virtual IntegralOperator::kind getKind() const override

Kind.

inline virtual model_type getType() const override

Type.

void initInfluence()

Initialize influence coefficients.

template<typename Functor>
void initFromFunctor(Functor func)

template<typename Functor>
void fourierApply(Functor func, GridBase<Real> &in, GridBase<Real> &out) const

Apply a functor in Fourier space.

virtual Real getOperatorNorm() override

Compute L_2 norm of influence functions.

virtual std::pair<UInt, UInt> matvecShape() const override

Dense shape.

virtual GridBase<Real> matvec(GridBase<Real> &x) const override

Dense matvec.

Public Members

std::shared_ptr<GridHermitian<Real, bdim>> influence

mutable GridHermitian<Real, bdim> buffer

mutable std::unique_ptr<FFTEngine> engine

Private Types

using trait = model_type_traits<mtype>

Private Static Attributes

static constexpr UInt dim = trait::dimension

static constexpr UInt bdim = trait::boundary_dimension

static constexpr UInt comp = trait::components

namespace cufft

namespace fftw

namespace fftw_impl

Functions

template<typename T>
inline auto free(T *ptr)

Free memory.

inline auto init_threads()

Init FFTW with threads.

inline auto plan_with_nthreads(int nthreads)

Set number of threads.

inline auto cleanup_threads()

Cleanup threads.

inline auto plan_many_forward(int rank, const int *n, int howmany, double *in, const int *inembed, int istride, int idist, fftw_complex *out, const int *onembed, int ostride, int odist, unsigned flags)

inline auto plan_many_backward(int rank, const int *n, int howmany, fftw_complex *in, const int *inembed, int istride, int idist, double *out, const int *onembed, int ostride, int odist, unsigned flags)

inline auto plan_1d_forward(int n, double *in, fftw_complex *out, unsigned flags)

inline auto plan_1d_backward(int n, fftw_complex *in, double *out, unsigned flags)

inline auto plan_2d_forward(int n0, int n1, double *in, fftw_complex *out, unsigned flags)

inline auto plan_2d_backward(int n0, int n1, fftw_complex *out, double *in, unsigned flags)

inline auto execute(fftw_plan plan)

inline auto execute(fftw_plan plan, double *in, fftw_complex *out)

inline auto execute(fftw_plan plan, fftw_complex *in, double *out)

inline auto destroy(fftw_plan plan)

inline auto plan_many_forward(int rank, const int *n, int howmany, long double *in, const int *inembed, int istride, int idist, fftwl_complex *out, const int *onembed, int ostride, int odist, unsigned flags)

inline auto plan_many_backward(int rank, const int *n, int howmany, fftwl_complex *in, const int *inembed, int istride, int idist, long double *out, const int *onembed, int ostride, int odist, unsigned flags)

inline auto plan_1d_forward(int n, long double *in, fftwl_complex *out, unsigned flags)

inline auto plan_1d_backward(int n, fftwl_complex *in, long double *out, unsigned flags)

inline auto plan_2d_forward(int n0, int n1, long double *in, fftwl_complex *out, unsigned flags)

inline auto plan_2d_backward(int n0, int n1, fftwl_complex *out, long double *in, unsigned flags)

inline auto execute(fftwl_plan plan)

inline auto execute(fftwl_plan plan, long double *in, fftwl_complex *out)

inline auto execute(fftwl_plan plan, fftwl_complex *in, long double *out)

inline auto destroy(fftwl_plan plan)

inline auto plan_many_forward(int rank, const int *n, int howmany, float *in, const int *inembed, int istride, int idist, fftwf_complex *out, const int *onembed, int ostride, int odist, unsigned flags)

inline auto plan_many_backward(int rank, const int *n, int howmany, fftwf_complex *in, const int *inembed, int istride, int idist, float *out, const int *onembed, int ostride, int odist, unsigned flags)

inline auto plan_1d_forward(int n, float *in, fftwf_complex *out, unsigned flags)

inline auto plan_1d_backward(int n, fftwf_complex *in, float *out, unsigned flags)

inline auto plan_2d_forward(int n0, int n1, float *in, fftwf_complex *out, unsigned flags)

inline auto plan_2d_backward(int n0, int n1, fftwf_complex *out, float *in, unsigned flags)

inline auto execute(fftwf_plan plan)

inline auto execute(fftwf_plan plan, float *in, fftwf_complex *out)

inline auto execute(fftwf_plan plan, fftwf_complex *in, float *out)

inline auto destroy(fftwf_plan plan)

namespace mpi_dummy

Functions

inline void init()

inline void cleanup()

inline auto local_size_many(int rank, const std::ptrdiff_t *size, std::ptrdiff_t howmany)

namespace tamaas

Typedefs

template<typename T>
using Allocator = FFTWAllocator<T>

template<typename T, UInt n, UInt m>
using Matrix = Tensor<StaticMatrix, T, n, m>

template<typename T, UInt n>
using SymMatrix = Tensor<StaticSymMatrix, T, n>

template<typename T, UInt n>
using Vector = Tensor<StaticVector, T, n>

template<typename T, UInt n, UInt m>
using MatrixProxy = TensorProxy<StaticMatrix, T, n, m>

template<typename T, UInt n>
using SymMatrixProxy = TensorProxy<StaticSymMatrix, T, n>

template<typename T, UInt n>
using VectorProxy = TensorProxy<StaticVector, T, n>

using Real = double

default floating point type

using Int = int

default signed integer type

using UInt = std::make_unsigned_t<Int>

default unsigned integer type

template<typename T>
using complex = thrust::complex<T>

template complex wrapper

using Complex = complex<Real>

default floating point complex type

using random_engine = ::thrust::random::default_random_engine

Enums

enum class LogLevel

Log levels enumeration.

Values:

enumerator debug

enumerator info

enumerator warning

enumerator error

enum class operation

Enumeration of reduction operations.

Values:

enumerator plus

enumerator times

enumerator min

enumerator max

enum class integration_method

Integration method enumeration.

Values:

enumerator cutoff

enumerator linear

enum class model_type

Types for grid dimensions and number of components.

Values:

enumerator basic_1d

one component line

enumerator basic_2d

one component surface

enumerator surface_1d

two components line

enumerator surface_2d

three components surface

enumerator volume_1d

two components volume

enumerator volume_2d

three components volume

Functions

void eigenvalues(model_type type, GridBase<Real> &eigs, const GridBase<Real> &field)

void vonMises(model_type type, GridBase<Real> &eigs, const GridBase<Real> &field)

void deviatoric(model_type type, GridBase<Real> &dev, const GridBase<Real> &field)

template<typename Compute>
void applyCompute(model_type type, GridBase<Real> &result, const GridBase<Real> &field)

template<typename T, UInt dim>
inline std::ostream &operator<<(std::ostream &stream, const Grid<T, dim> &_this)

template<template<typename, UInt> class Base, typename T, UInt base_dim, typename ...Args>
GridView<Base, T, base_dim, base_dim - sizeof...(Args)> make_view(Base<T, base_dim> &base, Args... indices)

template<template<typename, UInt> class Base, typename T, UInt base_dim>
GridView<Base, T, base_dim, base_dim> make_component_view(Base<T, base_dim> &base, UInt component)

std::ostream &operator<<(std::ostream &o, const LogLevel &val)

template<typename ...Ranges>
void checkLoopSize(Ranges&&... ranges)

template<typename LocalType, class Container>
std::enable_if_t<is_proxy<LocalType>::value, Range<LocalType, typename LocalType::value_type, LocalType::size>> range(Container &&cont)

Make range with proxy type.

template<typename LocalType, class Container>
std::enable_if_t<not is_proxy<LocalType>::value, Range<LocalType, LocalType, 1>> range(Container &&cont)

Make range with standard type.

template<typename DT1, typename ST1, typename DT2, typename ST2, UInt dim>
Vector<decltype(DT1(0) + DT2(0)), dim> operator+(const StaticVector<DT1, ST1, dim> &a, const StaticVector<DT2, ST2, dim> &b)

template<typename DT1, typename ST1, typename DT2, typename ST2, UInt dim>
Vector<decltype(DT1(0) - DT2(0)), dim> operator-(const StaticVector<DT1, ST1, dim> &a, const StaticVector<DT2, ST2, dim> &b)

template<typename DT1, typename ST1, UInt dim>
Vector<decltype(DT1(0)), dim> operator-(const StaticVector<DT1, ST1, dim> &a)

template<typename DT1, typename ST1, typename DT2, typename ST2, UInt n, UInt m>
Matrix<decltype(DT1(0) + DT2(0)), n, m> operator+(const StaticMatrix<DT1, ST1, n, m> &a, const StaticMatrix<DT2, ST2, n, m> &b)

template<typename DT1, typename ST1, typename DT2, typename ST2, UInt n, UInt m>
Matrix<decltype(DT1(0) - DT2(0)), n, m> operator-(const StaticMatrix<DT1, ST1, n, m> &a, const StaticMatrix<DT2, ST2, n, m> &b)

template<typename DT1, typename ST1, UInt n, UInt m>
Matrix<decltype(DT1(0)), n, m> operator-(const StaticMatrix<DT1, ST1, n, m> &a)

template<typename DT1, typename ST1, typename DT2, typename ST2, UInt n>
SymMatrix<decltype(DT1(0) + DT2(0)), n> operator+(const StaticSymMatrix<DT1, ST1, n> &a, const StaticSymMatrix<DT2, ST2, n> &b)

template<typename DT1, typename ST1, typename DT2, typename ST2, UInt n>
SymMatrix<decltype(DT1(0) - DT2(0)), n> operator-(const StaticSymMatrix<DT1, ST1, n> &a, const StaticSymMatrix<DT2, ST2, n> &b)

template<typename DT1, typename ST1, UInt dim>
SymMatrix<decltype(DT1(0)), dim> operator-(const StaticSymMatrix<DT1, ST1, dim> &a)

template<typename DT, typename ST, typename T, UInt n, typename = std::enable_if_t<is_arithmetic<T>::value>>
Vector<decltype(DT(0) * T(0)), n> operator*(const StaticVector<DT, ST, n> &a, const T &b)

template<typename DT, typename ST, typename T, UInt n, typename = std::enable_if_t<is_arithmetic<T>::value>>
Vector<decltype(DT(0) * T(0)), n> operator*(const T &b, const StaticVector<DT, ST, n> &a)

template<typename DT, typename ST, typename T, UInt n, UInt m, typename = std::enable_if_t<is_arithmetic<T>::value>>
Matrix<decltype(DT(0) * T(0)), n, m> operator*(const StaticMatrix<DT, ST, n, m> &a, const T &b)

template<typename DT, typename ST, typename T, UInt n, UInt m, typename = std::enable_if_t<is_arithmetic<T>::value, void>>
Matrix<decltype(DT(0) * T(0)), n, m> operator*(const T &b, const StaticMatrix<DT, ST, n, m> &a)

template<typename DT, typename ST, typename T, UInt n, typename = std::enable_if_t<is_arithmetic<T>::value>>
SymMatrix<decltype(DT(0) * T(0)), n> operator*(const StaticSymMatrix<DT, ST, n> &a, const T &b)

template<typename DT, typename ST, typename T, UInt n, typename = std::enable_if_t<is_arithmetic<T>::value>>
SymMatrix<decltype(DT(0) * T(0)), n> operator*(const T &b, const StaticSymMatrix<DT, ST, n> &a)

template<typename DT1, typename ST1, typename DT2, typename ST2, UInt n, UInt m>
Vector<decltype(DT1(0) * DT2(0)), n> operator*(const StaticMatrix<DT1, ST1, n, m> &a, const StaticVector<DT2, ST2, m> &b)

Matrix-vector multiplication.

template<typename DT1, typename ST1, typename DT2, typename ST2, UInt n, UInt m, UInt l>
Matrix<decltype(DT1(0) * DT2(0)), n, m> operator*(const StaticMatrix<DT1, ST1, n, l> &a, const StaticMatrix<DT2, ST2, l, m> &b)

Matrix-matrix multiplication.

template<typename DT1, typename ST1, typename DT2, typename ST2, UInt n, UInt m>
Matrix<decltype(DT1(0) * DT2(0)), n, m> outer(const StaticVector<DT1, ST1, n> &a, const StaticVector<DT2, ST2, m> &b)

template<typename DT, typename ST, UInt n>
Matrix<std::remove_cv_t<DT>, n, n> dense(const StaticSymMatrix<DT, ST, n> &m)

template<typename DT, typename ST, UInt n>
auto dense(const StaticVector<DT, ST, n> &v) -> Vector<DT, n>

template<typename DT, typename ST, UInt n>
SymMatrix<std::remove_cv_t<DT>, n> symmetrize(const StaticMatrix<DT, ST, n, n> &m)

template<typename DT, typename ST>
Vector<std::remove_cv_t<DT>, 3> invariants(const StaticSymMatrix<DT, ST, 3> &m)

template<typename DT, typename ST>
Vector<std::remove_cv_t<DT>, 3> eigenvalues(const StaticSymMatrix<DT, ST, 3> &m)

void initialize(UInt num_threads = 0)

initialize tamaas (0 threads => let OMP_NUM_THREADS decide)

void finalize()

cleanup tamaas

template<class U, class V = U>
U exchange(U &obj, V &&new_value)

CUDA-compatible exchange function.

void solve(IntegralOperator::kind kind, const std::map<IntegralOperator::kind, std::shared_ptr<IntegralOperator>> &operators, GridBase<Real> &input, GridBase<Real> &output)

template<model_type mtype, IntegralOperator::kind otype>
void registerWestergaardOperator(std::map<IntegralOperator::kind, std::shared_ptr<IntegralOperator>> &operators, Model &model)

Real boussinesq(Real x, Real y, Real a, Real b)

Square patch pressure solution, Johnson (1985) page 54.

BOOST_PP_SEQ_FOR_EACH (INSTANTIATE_HOOKE, ~,(model_type::basic_1d)(model_type::basic_2d)(model_type::surface_1d)(model_type::surface_2d)(model_type::volume_1d)(model_type::volume_2d))

std::ostream &operator<<(std::ostream &o, const IntegralOperator::kind &val)

std::ostream &operator<<(std::ostream &o, const Model &_this)

template<bool boundary, typename T>
std::unique_ptr<GridBase<T>> allocateGrid(Model &model)

template<bool boundary, typename T>
std::unique_ptr<GridBase<T>> allocateGrid(Model &model, UInt nc)

inline ModelDumper &operator<<(ModelDumper &dumper, Model &model)

template<typename Abstract, template<model_type> class Concrete, class ...Args>
decltype(auto) createFromModelType(model_type type, Args&&... args)

inline std::ostream &operator<<(std::ostream &o, const model_type &val)

Print function for model_type.

template<class Function>
constexpr decltype(auto) model_type_dispatch(Function &&function, model_type type)

Static dispatch lambda to model types.

template<class Function>
constexpr decltype(auto) dimension_dispatch(Function &&function, UInt dim)

Static dispatch lambda to dimensions.

template<model_type type, bool boundary, typename T, template<typename, UInt> class GridType = Grid, class Container = void>
std::unique_ptr<GridType<T, detail::dim_choice<type, boundary>::value>> allocateGrid(Container &&n, UInt nc)

Allocate a Grid unique_ptr.

template<bool boundary, typename T, typename Container>
decltype(auto) allocateGrid(model_type type, Container &&n)

Helper function for grid allocation with model type.

template<bool boundary, typename T, typename Container>
decltype(auto) allocateGrid(model_type type, Container &&n, UInt nc)

Helper function for grid allocation with non-standard components.

Int wrap_pbc(Int i, Int n)

template<std::size_t dim>
std::array<UInt, dim> wrap_pbc(const std::array<Int, dim> &t, const std::array<Int, dim> &n)

template<std::size_t dim>
std::array<Int, dim> cast_int(const std::array<UInt, dim> &a)

auto factorize(Grid<Real, 2> A)

Crout(e) (Antoine… et Daniel…) factorization from https://en.wikipedia.org/wiki/Crout_matrix_decomposition

auto LUsubstitute(std::pair<Grid<Real, 2>, Grid<Real, 2>> LU, Grid<Real, 1> b)

PetscErrorCode form_residual(SNES, Vec x, Vec f, void *ctx)

PetscErrorCode form_jacobian(SNES, Vec, Mat, Mat, void*)

PetscErrorCode tangent_shell(Mat mat, Vec x, Vec y)

Variables

static complex<Real> dummy

namespace [anonymous]

namespace [anonymous]

namespace [anonymous]

namespace [anonymous]

namespace compute

namespace detail

Typedefs

template<model_type type>
using model_type_t = std::integral_constant<model_type, type>

Convert enum value to a type.

template<UInt dim>
using dim_t = std::integral_constant<UInt, dim>

Convert dim value to a type.

model_types_t = std::tuple< BOOST_PP_SEQ_ENUM(BOOST_PP_SEQ_FOR_EACH(MAKE_MODEL_TYPE, ~,(model_type::basic_1d)(model_type::basic_2d)(model_type::surface_1d)(model_type::surface_2d)(model_type::volume_1d)(model_type::volume_2d)))>

Enumeration of model types.

dims_t = std::tuple< BOOST_PP_SEQ_ENUM(BOOST_PP_SEQ_FOR_EACH(MAKE_DIM_TYPE, ~,(1)(2)(3)))>

Enumeration of dimension types.

Functions

template<class T>
void append_to_stream(std::ostream &s, T &&head)

template<class T, class ...Args>
void append_to_stream(std::ostream &s, T &&head, Args&&... tail)

template<class ...Args>
std::string concat_args(Args&&... args)

template<bool only_points = false, typename ...Grids>
UInt loopSize(Grids&&... grids)

template<typename ...Sizes>
void areAllEqual(bool, std::ptrdiff_t)

template<typename ...Sizes>
void areAllEqual(bool result, std::ptrdiff_t prev, std::ptrdiff_t current)

template<typename ...Sizes>
void areAllEqual(bool result, std::ptrdiff_t prev, std::ptrdiff_t current, Sizes... rest)

template<class Function, class DynamicType, class DefaultFunction, std::size_t... Is>
constexpr decltype(auto) static_switch_dispatch(const model_types_t&, Function &&function, const DynamicType &type, DefaultFunction &&default_function, std::index_sequence<Is...>)

Specialized static dispatch for all model types.

template<class Function, class DynamicType, class DefaultFunction, std::size_t... Is>
constexpr decltype(auto) static_switch_dispatch(const dims_t&, Function &&function, const DynamicType &dim, DefaultFunction &&default_function, std::index_sequence<Is...>)

Specialized static dispatch for all dimensions.

template<class TypeTuple, class Function, class DefaultFunction, class DynamicType>
constexpr decltype(auto) tuple_dispatch_with_default(Function &&function, DefaultFunction &&default_function, const DynamicType &type)

Dispatch to tuple of types with a default case.

template<class TypeTuple, class Function, class DynamicType>
constexpr decltype(auto) tuple_dispatch(Function &&function, const DynamicType &type)

Dispatch to tuple of types, error on default.

namespace functional

namespace influence

Functions

template<bool conjugate, UInt dim_q>
inline Vector<Complex, dim_q + 1> computeD(const VectorProxy<const Real, dim_q> &q)

template<UInt dim_q>
inline Vector<Complex, dim_q + 1> computeD2(const VectorProxy<const Real, dim_q> &q)

namespace [anonymous]

namespace iterator_

namespace mpi_dummy

Contains mock mpi functions.

Enums

enum class thread : int

Values:

enumerator single

enumerator funneled

enumerator serialized

enumerator multiple

Functions

inline bool initialized()

inline bool finalized()

inline int init(int*, char***)

inline int init_thread(int*, char***, thread, thread *provided)

inline int finalize()

inline void abort(int) noexcept

inline int rank(comm = comm::world())

inline int size(comm = comm::world())

template<operation op = operation::plus, typename T>
inline decltype(auto) reduce(T &&val, comm = comm::world())

template<operation op = operation::plus, typename T>
inline decltype(auto) allreduce(T &&val, comm = comm::world())

template<typename T>
inline decltype(auto) gather(const T *send, T *recv, int count, comm = comm::world())

template<typename T>
inline decltype(auto) scatter(const T *send, T *recv, int count, comm = comm::world())

template<typename T>
inline decltype(auto) scatterv(const T *send, const std::vector<int>&, const std::vector<int>&, T *recv, int recvcount, comm = comm::world())

template<typename T>
inline decltype(auto) bcast(T*, int, comm = comm::world())

file allocator.hh

#include “tamaas.hh”

#include “fftw/fftw_allocator.hh”

file array.hh

#include “allocator.hh”

#include “errors.hh”

#include “logger.hh”

#include “span.hh”

#include “tamaas.hh”

#include <memory>

#include <thrust/copy.h>

#include <thrust/fill.h>

#include <utility>

file computes.cpp

#include “computes.hh”

file computes.hh

#include “grid.hh”

#include “loop.hh”

#include “model_type.hh”

#include “ranges.hh”

#include “static_types.hh”

file cufft_engine.cpp

#include “cufft_engine.hh”

#include <algorithm>

#include <functional>

#include <numeric>

file cufft_engine.hh

#include “fft_engine.hh”

#include <cufft.h>

file unified_allocator.hh

#include “span.hh”

#include <cuda_runtime_api.h>

#include <memory>

file errors.hh

#include <sstream>

#include <stdexcept>

Defines

TAMAAS_LOCATION

TAMAAS_MSG(...)

TAMAAS_ASSERT(cond, ...)

file fft_engine.cpp

#include “fft_engine.hh”

#include “fftw/fftw_engine.hh”

Defines

inst(x)

file fft_engine.hh

#include “grid.hh”

#include “grid_base.hh”

#include “grid_hermitian.hh”

#include “partitioner.hh”

#include <algorithm>

#include <array>

#include <map>

#include <memory>

#include <string>

file fftw_allocator.hh

#include “span.hh”

#include <fftw3.h>

#include <memory>

file fftw_engine.cpp

#include “fftw_engine.hh”

#include <algorithm>

#include <functional>

#include <numeric>

file fftw_engine.hh

#include “fft_engine.hh”

#include “fftw/interface.hh”

file interface.hh

#include “mpi/interface.hh”

#include “interface_impl.hh”

Defines

FFTW_ESTIMATE

file interface.hh

#include “mpi_interface.hh”

#include <cstdlib>

#include <numeric>

#include <stdexcept>

#include <tuple>

file interface_impl.hh

#include <cstddef>

#include <fftw3.h>

#include <functional>

#include <numeric>

#include <utility>

file fftw_mpi_engine.cpp

#include “fftw/mpi/fftw_mpi_engine.hh”

#include “fftw/interface.hh”

#include “logger.hh”

#include “mpi_interface.hh”

#include “partitioner.hh”

#include <algorithm>

file fftw_mpi_engine.hh

#include “fftw/fftw_engine.hh”

#include “fftw/interface.hh”

#include “grid.hh”

#include “grid_hermitian.hh”

#include <map>

file grid.cpp

#include “grid.hh”

#include “tamaas.hh”

#include <algorithm>

#include <complex>

#include <cstring>

Defines

GRID_INSTANCIATE_TYPE(type)

Class instanciation.

file grid.hh

#include “grid_base.hh”

#include “tamaas.hh”

#include <array>

#include <numeric>

#include <utility>

#include <vector>

#include “grid_tmpl.hh”

file grid_base.hh

#include “array.hh”

#include “iterator.hh”

#include “loop.hh”

#include “mpi_interface.hh”

#include “static_types.hh”

#include “tamaas.hh”

#include <cstddef>

#include <limits>

#include <utility>

#include <vector>

Defines

VEC_OPERATOR(op)

SCALAR_OPERATOR(op)

BROADCAST_OPERATOR(op)

Broadcast operators.

SCALAR_OPERATOR_IMPL(op)

VEC_OPERATOR_IMPL(op)

BROADCAST_OPERATOR_IMPL(op)

file grid_hermitian.cpp

#include “grid_hermitian.hh”

Defines

GRID_HERMITIAN_INSTANCIATE(type)

file grid_hermitian.hh

#include “grid.hh”

#include “tamaas.hh”

#include <complex>

#include <type_traits>

#include <vector>

file grid_tmpl.hh

#include “grid.hh”

#include “tamaas.hh”

file grid_view.hh

#include “grid.hh”

#include “tamaas.hh”

#include <vector>

file iterator.hh

#include “tamaas.hh”

#include <cstddef>

#include <iterator>

#include <thrust/iterator/iterator_categories.h>

#include <utility>

#include <vector>

file logger.cpp

#include “logger.hh”

#include “mpi_interface.hh”

#include <cstdlib>

#include <iostream>

#include <map>

file logger.hh

#include “tamaas.hh”

#include <sstream>

file loop.cpp

#include “loop.hh”

#include “tamaas.hh”

file loop.hh

#include “loops/apply.hh”

#include “loops/loop_utils.hh”

#include “mpi_interface.hh”

#include “ranges.hh”

#include “tamaas.hh”

#include <thrust/execution_policy.h>

#include <thrust/for_each.h>

#include <thrust/iterator/counting_iterator.h>

#include <thrust/iterator/zip_iterator.h>

#include <thrust/transform_reduce.h>

#include <thrust/tuple.h>

#include <thrust/version.h>

#include <type_traits>

#include <utility>

file apply.hh

#include “tamaas.hh”

#include <cstddef>

#include <thrust/tuple.h>

#include <utility>

file loop_utils.hh

#include “errors.hh”

#include “tamaas.hh”

#include <limits>

#include <thrust/functional.h>

#include <type_traits>

file mpi_interface.cpp

#include “mpi_interface.hh”

file mpi_interface.hh

#include “static_types.hh”

#include “tamaas.hh”

#include <cstdlib>

#include <type_traits>

#include <vector>

Defines

MPI_ERR_TOPOLOGY

file partitioner.hh

#include “fftw/interface.hh”

#include “grid.hh”

#include “mpi_interface.hh”

#include “tamaas.hh”

#include <algorithm>

#include <array>

#include <cstdlib>

#include <functional>

file ranges.hh

#include “errors.hh”

#include “iterator.hh”

#include “mpi_interface.hh”

#include “static_types.hh”

file span.hh

#include “tamaas.hh”

#include <cstddef>

#include <iterator>

#include <type_traits>

file static_types.hh

#include “tamaas.hh”

#include <thrust/detail/config/host_device.h>

#include <thrust/sort.h>

#include <type_traits>

Defines

VECTOR_OP(op)

SCALAR_OP(op)

file statistics.cpp

#include “statistics.hh”

#include “fft_engine.hh”

#include “loop.hh”

#include “static_types.hh”

Variables

std::array<UInt, dim> exponent

file statistics.hh

#include “fft_engine.hh”

#include “grid.hh”

file tamaas.cpp

#include “tamaas.hh”

#include “errors.hh”

#include “fftw/interface.hh”

#include “logger.hh”

#include “mpi_interface.hh”

Variables

static const entry_exit_points singleton

file tamaas.hh

#include <exception>

#include <iostream>

#include <memory>

#include <string>

#include <type_traits>

#include <thrust/complex.h>

#include <thrust/random.h>

Defines

TAMAAS_USE_FFTW

TAMAAS_FFTW_BACKEND_OMP

TAMAAS_FFTW_BACKEND_THREADS

TAMAAS_FFTW_BACKEND_NONE

TAMAAS_LOOP_BACKEND_OMP

TAMAAS_LOOP_BACKEND_TBB

TAMAAS_LOOP_BACKEND_CPP

TAMAAS_LOOP_BACKEND_CUDA

TAMAAS_LOOP_BACKEND

TAMAAS_FFTW_BACKEND

THRUST_DEVICE_SYSTEM

TAMAAS_ACCESSOR(var, type, name)

Convenience macros.

CUDA_LAMBDA

Cuda specific definitions.

TAMAAS_REAL_TYPE

Common types definitions.

TAMAAS_INT_TYPE

file adhesion_functional.cpp

#include “adhesion_functional.hh”

file adhesion_functional.hh

#include “functional.hh”

#include <map>

file be_engine.cpp

#include “be_engine.hh”

#include “logger.hh”

#include “model.hh”

file be_engine.hh

#include “integral_operator.hh”

#include “model_type.hh”

#include “westergaard.hh”

file boussinesq.cpp

#include “boussinesq.hh”

#include “boussinesq_helper.hh”

#include “influence.hh”

#include “model.hh”

file boussinesq.hh

#include “grid_hermitian.hh”

#include “model_type.hh”

#include “volume_potential.hh”

file boussinesq_helper.hh

#include “grid.hh”

#include “grid_hermitian.hh”

#include “influence.hh”

#include “integration/accumulator.hh”

#include “kelvin_helper.hh”

#include “model.hh”

#include “model_type.hh”

#include <vector>

file dcfft.cpp

#include “dcfft.hh”

#include “model.hh”

#include <cmath>

file dcfft.hh

#include “westergaard.hh”

file elastic_functional.cpp

#include “elastic_functional.hh”

file elastic_functional.hh

#include “functional.hh”

#include “model.hh”

#include “tamaas.hh”

file field_container.hh

#include “grid.hh”

#include “model_type.hh”

#include <algorithm>

#include <boost/variant.hpp>

#include <memory>

#include <string>

#include <unordered_map>

file functional.hh

#include “be_engine.hh”

#include “tamaas.hh”

file hooke.cpp

#include “hooke.hh”

#include “influence.hh”

#include “loop.hh”

#include “model.hh”

#include “static_types.hh”

#include <boost/preprocessor/seq.hpp>

Defines

INSTANTIATE_HOOKE(r, _, type)

file hooke.hh

#include “integral_operator.hh”

#include “model_type.hh”

file influence.hh

#include “loop.hh”

#include “static_types.hh”

#include <type_traits>

file integral_operator.cpp

#include “integral_operator.hh”

#include “model.hh”

#include <map>

#include <ostream>

file integral_operator.hh

#include “field_container.hh”

#include “grid_base.hh”

#include “model_type.hh”

file accumulator.hh

#include “grid_hermitian.hh”

#include “integrator.hh”

#include “model_type.hh”

#include “static_types.hh”

#include <array>

#include <thrust/iterator/zip_iterator.h>

#include <vector>

file element.cpp

#include “element.hh”

file element.hh

#include “tamaas.hh”

#include <expolit/expolit>

file integrator.hh

#include “element.hh”

#include <expolit/expolit>

Defines

BOUNDS

file kelvin.cpp

#include “kelvin.hh”

#include “logger.hh”

file kelvin.hh

#include “grid_hermitian.hh”

#include “influence.hh”

#include “integration/accumulator.hh”

#include “kelvin_helper.hh”

#include “model_type.hh”

#include “volume_potential.hh”

file kelvin_helper.hh

#include “grid.hh”

#include “grid_hermitian.hh”

#include “influence.hh”

#include “integration/accumulator.hh”

#include “logger.hh”

#include “model.hh”

#include “model_type.hh”

#include <tuple>

file internal.hh

#include “grid.hh”

#include <memory>

file isotropic_hardening.cpp

#include “isotropic_hardening.hh”

#include “influence.hh”

#include “tamaas.hh”

file isotropic_hardening.hh

#include “grid.hh”

#include “influence.hh”

#include “internal.hh”

#include “material.hh”

#include “model.hh”

#include “model_type.hh”

#include “static_types.hh”

file linear_elastic.cpp

#include “linear_elastic.hh”

file linear_elastic.hh

#include “material.hh”

file material.hh

#include “grid.hh”

#include “model.hh”

#include “model_type.hh”

file meta_functional.cpp

#include “meta_functional.hh”

file meta_functional.hh

#include “functional.hh”

#include “tamaas.hh”

#include <list>

#include <memory>

file mindlin.cpp

#include “mindlin.hh”

#include “boussinesq_helper.hh”

#include “influence.hh”

#include “kelvin_helper.hh”

#include “model_type.hh”

file mindlin.hh

#include “grid_hermitian.hh”

#include “kelvin.hh”

#include “model_type.hh”

#include “volume_potential.hh”

file model.cpp

#include “model.hh”

#include “be_engine.hh”

#include “logger.hh”

file model.hh

#include “be_engine.hh”

#include “field_container.hh”

#include “grid_base.hh”

#include “integral_operator.hh”

#include “model_dumper.hh”

#include “model_type.hh”

#include “tamaas.hh”

#include <algorithm>

#include <memory>

#include <vector>

file model_dumper.hh

file model_factory.cpp

#include “model_factory.hh”

#include “dcfft.hh”

#include “materials/isotropic_hardening.hh”

#include “model_template.hh”

#include <functional>

Defines

CAST(derivative)

file model_factory.hh

#include “be_engine.hh”

#include “model.hh”

#include “model_type.hh”

#include “residual.hh”

#include <vector>

file model_template.cpp

#include “model_template.hh”

#include “computes.hh”

#include “hooke.hh”

#include “influence.hh”

#include “kelvin.hh”

#include “partitioner.hh”

#include “westergaard.hh”

Defines

CAST(derivative, ptr)

file model_template.hh

#include “grid_view.hh”

#include “model.hh”

#include “model_type.hh”

file model_type.cpp

#include “model_type.hh”

file model_type.hh

#include “grid.hh”

#include “grid_base.hh”

#include “static_types.hh”

#include “tamaas.hh”

#include <algorithm>

#include <boost/preprocessor/cat.hpp>

#include <boost/preprocessor/seq.hpp>

#include <boost/preprocessor/stringize.hpp>

#include <memory>

Defines

MODEL_TYPE_TRAITS_MACRO(type, dim, comp, bdim)

TAMAAS_MODEL_TYPES

MAKE_MODEL_TYPE(r, x, type)

MAKE_DIM_TYPE(r, x, dim)

PRINT_MODEL_TYPE(r, data, type)

SWITCH_DISPATCH_CASE(r, data, type)

SWITCH_DISPATCH_CASE(r, data, dim)

file residual.cpp

#include “residual.hh”

#include “grid_view.hh”

#include “model_factory.hh”

#include “model_type.hh”

#include <list>

#include <memory>

file residual.hh

#include “boussinesq.hh”

#include “materials/material.hh”

#include “mindlin.hh”

#include “model_type.hh”

#include <unordered_set>

file volume_potential.cpp

#include “volume_potential.hh”

#include “model.hh”

#include <algorithm>

file volume_potential.hh

#include “fft_engine.hh”

#include “grid_hermitian.hh”

#include “grid_view.hh”

#include “integral_operator.hh”

#include “logger.hh”

#include “model_type.hh”

#include <functional>

file westergaard.cpp

#include “grid_hermitian.hh”

#include “grid_view.hh”

#include “influence.hh”

#include “loop.hh”

#include “model.hh”

#include “model_type.hh”

#include “static_types.hh”

#include “westergaard.hh”

#include <functional>

#include <numeric>

file westergaard.hh

#include “fft_engine.hh”

#include “grid_hermitian.hh”

#include “integral_operator.hh”

#include “model_type.hh”

#include “tamaas.hh”

file flood_fill.cpp

#include “flood_fill.hh”

#include “partitioner.hh”

#include <algorithm>

#include <limits>

#include <queue>

file flood_fill.hh

#include “grid.hh”

#include <list>

file anderson.cpp

#include “anderson.hh”

#include <algorithm>

#include <iomanip>

file anderson.hh

#include “epic.hh”

#include <deque>

file beck_teboulle.cpp

#include “beck_teboulle.hh”

#include “logger.hh”

#include <iomanip>

file beck_teboulle.hh

#include “kato.hh”

file condat.cpp

#include “condat.hh”

#include “logger.hh”

#include <iomanip>

file condat.hh

#include “kato.hh”

file contact_solver.cpp

#include “contact_solver.hh”

#include “logger.hh”

#include <iomanip>

#include <iostream>

file contact_solver.hh

#include “meta_functional.hh”

#include “model.hh”

#include “tamaas.hh”

file dfsane_solver.cpp

#include “dfsane_solver.hh”

file dfsane_solver.hh

#include “ep_solver.hh”

#include “grid_base.hh”

#include “residual.hh”

#include <deque>

#include <functional>

#include <utility>

file ep_solver.cpp

#include “ep_solver.hh”

#include “model_type.hh”

file ep_solver.hh

#include “grid_base.hh”

#include “residual.hh”

file epic.cpp

#include “epic.hh”

#include “logger.hh”

file epic.hh

#include “contact_solver.hh”

#include “ep_solver.hh”

#include “model.hh”

file kato.cpp

#include “kato.hh”

#include “elastic_functional.hh”

#include “logger.hh”

#include “loop.hh”

#include <iomanip>

#include <iostream>

#include <iterator>

file kato.hh

#include “contact_solver.hh”

#include “meta_functional.hh”

#include “model_type.hh”

#include “static_types.hh”

#include “tamaas.hh”

file kato_saturated.cpp

#include “kato_saturated.hh”

#include “logger.hh”

#include <iomanip>

#include <limits>

file kato_saturated.hh

#include “polonsky_keer_rey.hh”

#include <limits>

file petsc_solver.cpp

#include “petsc_solver.hh”

#include <petscsystypes.h>

Defines

chk(error)

file petsc_solver.hh

#include “ep_solver.hh”

#include “residual.hh”

#include <petscmat.h>

#include <petscoptions.h>

#include <petscsnes.h>

#include <petscsys.h>

#include <petscvec.h>

#include <string>

#include <vector>

file polonsky_keer_rey.cpp

#include “polonsky_keer_rey.hh”

#include “elastic_functional.hh”

#include “logger.hh”

#include “loop.hh”

#include “model_type.hh”

#include <iomanip>

file polonsky_keer_rey.hh

#include “contact_solver.hh”

#include “grid_view.hh”

#include “meta_functional.hh”

#include “westergaard.hh”

Defines

WESTERGAARD(type, kind, desc)

file polonsky_keer_tan.cpp

#include “polonsky_keer_tan.hh”

#include <iomanip>

file polonsky_keer_tan.hh

#include “kato.hh”

file filter.hh

#include “fft_engine.hh”

#include “grid.hh”

#include “grid_hermitian.hh”

file isopowerlaw.cpp

#include “isopowerlaw.hh”

#include <map>

file isopowerlaw.hh

#include “filter.hh”

#include “grid_hermitian.hh”

#include “static_types.hh”

file regularized_powerlaw.cpp

#include “regularized_powerlaw.hh”

file regularized_powerlaw.hh

#include “filter.hh”

#include “grid_hermitian.hh”

#include “static_types.hh”

file surface_generator.cpp

#include “surface_generator.hh”

#include “partitioner.hh”

#include <algorithm>

file surface_generator.hh

#include “grid.hh”

#include <array>

file surface_generator_filter.cpp

#include “surface_generator_filter.hh”

#include <iostream>

file surface_generator_filter.hh

#include “fft_engine.hh”

#include “filter.hh”

#include “partitioner.hh”

#include “surface_generator.hh”

#include “tamaas.hh”

file surface_generator_random_phase.cpp

#include “surface_generator_random_phase.hh”

#include <iostream>

file surface_generator_random_phase.hh

#include “filter.hh”

#include “surface_generator_filter.hh”

#include “tamaas.hh”

file tamaas_info.hh

#include <string>

dir /home/docs/checkouts/readthedocs.org/user_builds/tamaas/checkouts/latest/src/core

dir /home/docs/checkouts/readthedocs.org/user_builds/tamaas/checkouts/latest/src/core/cuda

dir /home/docs/checkouts/readthedocs.org/user_builds/tamaas/checkouts/latest/src/core/fftw

dir /home/docs/checkouts/readthedocs.org/user_builds/tamaas/checkouts/latest/src/model/integration

dir /home/docs/checkouts/readthedocs.org/user_builds/tamaas/checkouts/latest/src/core/loops

dir /home/docs/checkouts/readthedocs.org/user_builds/tamaas/checkouts/latest/src/model/materials

dir /home/docs/checkouts/readthedocs.org/user_builds/tamaas/checkouts/latest/src/model

dir /home/docs/checkouts/readthedocs.org/user_builds/tamaas/checkouts/latest/src/core/fftw/mpi

dir /home/docs/checkouts/readthedocs.org/user_builds/tamaas/checkouts/latest/src/percolation

dir /home/docs/checkouts/readthedocs.org/user_builds/tamaas/checkouts/latest/src/solvers

dir /home/docs/checkouts/readthedocs.org/user_builds/tamaas/checkouts/latest/src

dir /home/docs/checkouts/readthedocs.org/user_builds/tamaas/checkouts/latest/src/surface

page index

Introduction

Tamaas is a spectral-integral-equation based contact library. It is made with love to be fast and friendly!

Author

Lucas Frérot lucas.frerot@imtek.uni-freiburg.de

Author

Guillaume Anciaux guillaume.anciaux@epfl.ch

Author

Valentine Rey valentine.rey@univ-nantes.fr

Author

Son Pham-Ba son.phamba@epfl.ch

Author

Jean-François Molinari jean-francois.molinari@epfl.ch

License

Copyright (©) 2016-2024 EPFL (École Polytechnique Fédérale de Lausanne), Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides) Copyright (©) 2020-2024 Lucas Frérot

This program is free software: you can redistribute it and/or modify it under the terms of the GNU Affero General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Affero General Public License for more details.

You should have received a copy of the GNU Affero General Public License along with this program. If not, see https://www.gnu.org/licenses/.

Indices and tables

• Index

• Module Index

• Search Page