Developer Guide

This section purports to document the SfePy internals. It is mainly useful for those who wish to contribute to the development of SfePy and understand the inner workings of the code.

We use git to track source code, documentation, examples, and other files related to the project.

It is not necessary to learn git in order to contribute to SfePy but we strongly suggest you do so as soon as possible - it is an extremely useful tool not just for writing code, but also for tracking revisions of articles, Ph.D. theses, books, … it will also look well in your CV :-) It is also much easier for us to integrate changes that are in form of a github pull request than in another form.

Retrieving the Latest Code

The first step is to obtain the latest development version of the code from the SfePy git repository:

git clone git://github.com/sfepy/sfepy.git

For development, it is preferable to build the extension modules in place (see Compilation of C Extension Modules):

python setup.py build_ext --inplace

On Unix-like systems, you can simply type make in the top-level folder to build in-place.

After the initial compilation, or after making changes, do not forget to run the tests, see Testing Installation.

SfePy Directory Structure

Here we list and describe the directories that are in the main sfepy directory.

Top directory structure.

name

description

build/

directory created by the build process (generated)

doc/

source files of this documentation

meshes/

finite element mesh files in various formats shared by the examples

output/

default output directory for storing results of the examples

sfepy/

the source code including examples and tests

tools/

various helper scripts (build, documentation generation etc.)

New users/developers (after going through the Tutorial) should explore the sfepy/examples/ directory. For developers, the principal directory is sfepy/, which has the following contents:

sfepy/ directory structure.

name

description

field-specific

applications/

top level application classes (e.g. PDESolverApp)

base/

common utilities and classes used by most of the other modules

discrete/

general classes and modules for describing a discrete problem, taking care of boundary conditions, degrees of freedom, approximations, variables, equations, meshes, regions, quadratures, etc.

Discretization-specific classes are in subdirectories:

  • common/ - common parent classes for discretization-specific classes

  • fem/ - finite element specific classes

  • iga/ - isogeometric analysis specific classes

examples/

the examples using both the declarative and imperative problem description API

homogenization/

the homogenization engine and supporting modules - highly specialized code, one of the reasons of SfePy existence

linalg/

linear algebra functions not covered by NumPy and SciPy

mechanics/

modules for (continuum) mechanics: elastic constant conversions, tensor, units utilities, etc.

mesh/

some utilities to interface with tetgen and triangle mesh generators

parallel/

modules supporting parallel assembling and solution of problems

postprocess/

Matplotlib and VTK based post-processing modules

scripts/

the main as well as auxiliary scripts

solvers/

interface classes to various internal/external solvers (linear, nonlinear, eigenvalue, optimization, time stepping)

terms/

implementation of the terms (weak formulation integrals), see Term Overview

tests/

the tests

The directories in the “field-specific” column are mostly interesting for specialists working in the respective fields.

The discrete/ is the heart of the code, while the terms/ contains the particular integral forms usable to build equations - new term writers should look there.

Exploring the Code

It is convenient to install IPython to have the tab completion available. Moreover, all SfePy classes can be easily examined by printing them:

 1In [1]: from sfepy.discrete.fem import Mesh
 2
 3In [2]: mesh = Mesh.from_file('meshes/2d/rectangle_tri.mesh')
 4sfepy: reading mesh [line2, tri3, quad4, tetra4, hexa8] (meshes/2d/rectangle_tri.mesh)...
 5sfepy: ...done in 0.00 s
 6
 7In [3]: print(mesh)
 8Mesh:meshes/2d/rectangle_tri
 9  cmesh:
10    CMesh: n_coor: 258, dim 2, tdim: 2, n_el 454
11  descs:
12    list: ['2_3']
13  dim:
14    2
15  dims:
16    list: [2]
17  io:
18    None
19  n_el:
20    454
21  n_nod:
22    258
23  name:
24    meshes/2d/rectangle_tri
25  nodal_bcs:
26    dict with keys: []

We recommend going through the interactive example in the tutorial Interactive Example: Linear Elasticity in this way, printing all the variables.

Another useful tool is the debug() function, that can be used as follows:

from sfepy.base.base import debug; debug()

Try to use it in the examples with user defined functions to explore their parameters etc. It works best with IPython installed, as then the tab completion is available also when debugging.

How to Contribute

Read this section if you wish to contribute some work to the SfePy project - everyone is welcome to contribute. Contributions can be made in a variety of forms, not just code. Reporting bugs and contributing to the documentation, tutorials, and examples is in great need!

Below we describe

  1. where to report problems or find existing issues and additional development suggestions

  2. what to do to apply changes/fixes

  3. what to do after you made your changes/fixes

Reporting problems

Reporting a bug is the first way in which to contribute to an open source project

Short version: go to the main SfePy site and follow the links given there.

When you encounter a problem, try searching that site first - an answer may already be posted in the SfePy mailing list (to which we suggest you subscribe…), or the problem might have been added to the SfePy issues. As is true in any open source project, doing your homework by searching for existing known problems greatly reduces the burden on the developers by eliminating duplicate issues. If you find your problem already exists in the issue tracker, feel free to gather more information and append it to the issue. In case the problem is not there, create a new issue with proper labels for the issue type and priority, and/or ask us using the mailing list.

Note: A google account (e.g., gmail account) is needed to join the mailing list. A github account is needed for working with the source code repository and issues.

Note: When reporting a problem, try to provide as much information as possible concerning the version of SfePy, the OS / Linux distribution, and the versions of Python, NumPy and SciPy, and other prerequisites. The versions found on your system can be printed by running:

python setup.py --help

If you are a new user, please let us know what difficulties you have with this documentation. We greatly welcome a variety of contributions not limited to code only.

Contributing changes

Note: To avoid duplicating work, it is highly advised that you contact the developers on the mailing list or create an enhancement issue before starting work on a non-trivial feature.

Before making any changes, read the Notes on commits and patches.

Using git and github

The preferred way to contribute to SfePy is to fork the main repository on github, then submit a “pull request” (PR):

  1. Create a github account if you do not already have one.

  2. Fork the project repository: click on the “Fork” button near the top of the sfepy git repository page. This creates a copy of the repository under your account on the github server.

  3. Clone your fork to your computer:

    git clone git@github.com:YourLogin/sfepy.git

  4. If you have never used git before, introduce yourself to git and make (optionally) some handy aliases either in .gitconfig in your home directory (global settings for all your git projects), or directly in .git/config in the repository:

     1[user]
 2    email = mail@mail.org
 3    name = Name Surname
 4
 5[color]
 6    ui = auto
 7    interactive = true
 8
 9[alias]
10    ci = commit
11    di = diff --color-words
12    st = status
13    co = checkout

  5. Create a feature branch to hold your changes:

    git checkout -b my-feature

    Then you can start to make your changes. Do not work in the master branch!

  6. Modify some files and use git to track your local changes. The changed added/modified files can be listed using:

    git status

    and the changes can be reviewed using:

    git diff

    A more convenient way of achieving the above is to run:

    gitk --all

    in order to visualize of project history (all branches). There are other GUIs for this purpose, e.g. qgit. You may need to install those tools, as they usually are not installed with git by default. Record a set of changes by:

    1# schedule some of the changed files for the next commit
2git add file1 file2 ...
3# an editor will pop up where you should describe the commit
4git commit

    We recommend git gui command in case you want to add and commit only some changes in a modified file.

    Note: Do not be afraid to experiment - git works with your local copy of the repository, so it is not possible to damage the master repository. It is always possible to re-clone a fresh copy, in case you do something that is really bad.

  7. The commit(s) now reflect changes, but only in your local git repository. To update your github repository with your new commit(s), run:

    git push origin my-feature:my-feature

  8. Finally, when your feature is ready, and all tests pass, go to the github page of your sfepy repository fork, and click “Pull request” to send your changes to the maintainers for review. Continuous integration (CI) will run and check that the changes pass tests on Windows, Linux and Mac using Github Actions. The results will be displayed in the Pull Request discussion. The CI setup is located in the file .github/workflows/build_and_test_matrix.yml. It is recommended to check that your contribution complies with the Notes on commits and patches.

In the above setup, your origin remote repository points to YourLogin/sfepy.git. If you wish to fetch/merge from the main repository instead of your forked one, you will need to add another remote to use instead of origin. The main repository is usually called “upstream”. To add it, type:

git remote add upstream https://github.com/sfepy/sfepy.git

To synchronize your repository with the upstream, proceed as follows:

  1. Fetch the upstream changes:

    git fetch upstream

    Never start with git pull upstream!

  2. Check the changes of the upstream master branch. You can use gitk --all to visualize all your and remote branches. The upstream master is named remotes/upstream/master.

  3. Make sure all your local changes are either committed in a feature branch or stashed (see git stash). Then reset your master to the upstream master:

    git checkout master
git reset --hard upstream/master

    Warning The above will remove all your local commits in the master branch that are not in upstream/master, and also reset all the changes in your non-committed modified files!

    Optionally, the reset command can be run conveniently in gitk by right-clicking on a commit you want to reset the current branch onto.

  4. Optionally, rebase your feature branch onto the upstream master:

    git checkout my-feature
git rebase upstream/master

    This is useful, for example, when the upstream master contains a change you need in your feature branch.

For additional information, see, for example, the gitwash git tutorial, or its incarnation NumPy gitwash.

Notes on commits and patches

  • Follow our Coding style.

  • Do not use lines longer than 79 characters (exception: tables of values, e.g., quadratures).

  • Write descriptive docstrings in correct style, see Docstring standard.

  • There should be one patch for one topic - do not mix unrelated things in one patch. For example, when you add a new function, then notice a typo in docstring in a nearby function and correct it, create two patches: one fixing the docstring, the other adding the new function.

  • The commit message and description should clearly state what the patch does. Try to follow the style of other commit messages. Some interesting notes can be found at tbaggery.com, namely that the commit message is better to be written in the present tense: “fix bug” and not “fixed bug”.

Without using git

Without using git, send the modified files to the SfePy mailing list or attach them using gist to the corresponding issue at the Issues web page. Do not forget to describe the changes properly, and to follow the spirit of Notes on commits and patches and the Coding style.

Coding style

All the code in SfePy should try to adhere to python style guidelines, see PEP-0008.

There are some additional recommendations:

  • Prefer whole words to abbreviations in public APIs - there is completion after all. If some abbreviation is needed (really too long name), try to make it as comprehensible as possible. Also check the code for similar names - try to name things consistently with the existing code. Examples:

    • yes: equation, transform_variables(), filename

    • rather not: eq, transvar(), fname

  • Functions have usually form <action>_<subject>() e.g.: save_data(), transform_variables(), do not use data_save(), variable_transform() etc.

  • Variables like V, c, A, b, x should be tolerated only locally when expressing mathematical ideas.

Really minor recommendations:

  • Avoid single letter names, if you can:

    • not even for loop variables - use e.g. ir, ic, … instead of i, j for rows and columns

    • not even in generators, as they “leak” (this is fixed in Python 3.x)

These are recommendations only, we will not refuse code just on the ground that it uses slightly different formatting, as long as it follows the PEP.

Note: some old parts of the code might not follow the PEP, yet. We fix them progressively as we update the code.

Docstring standard

We use sphinx with the numpydoc extension to generate this documentation. Refer to the sphinx site for the possible markup constructs.

Basically (with a little tweak), we try to follow the NumPy/SciPy docstring standard as described in NumPy documentation guide. See also the complete docstring example. It is exaggerated a bit to show all the possibilities. Use your common sense here - the docstring should be sufficient for a new user to use the documented object. A good way to remember the format is to type:

In [1]: import numpy as nm
In [2]: nm.sin?

in ipython. The little tweak mentioned above is the starting newline:

 1def function(arg1, arg2):
 2    """
 3    This is a function.
 4
 5    Parameters
 6    ----------
 7    arg1 : array
 8        The coordinates of ...
 9    arg2 : int
10        The dimension ...
11
12    Returns
13    -------
14    out : array
15       The resulting array of shape ....
16    """

It seems visually better than:

 1def function(arg1, arg2):
 2    """This is a function.
 3
 4    Parameters
 5    ----------
 6    arg1 : array
 7        The coordinates of ...
 8    arg2 : int
 9        The dimension ...
10
11    Returns
12    -------
13    out : array
14       The resulting array of shape ....
15    """

When using \mbox{\LaTeX} in a docstring, use a raw string:

1def function():
2    r"""
3    This is a function with :math:`\mbox{\LaTeX}` math:
4    :math:`\frac{1}{\pi}`.
5    """

to prevent Python from interpreting and consuming the backslashes in common escape sequences like ‘\n’, ‘\f’ etc.

How to Regenerate Documentation

The following steps summarize how to regenerate this documentation.

  1. Install sphinx, numpydoc, `sphinx-rtd-theme`_ and IPython. Do not forget to set the path to numpydoc in site_cfg.py if it is not installed in a standard location for Python packages on your platform. A recent \mbox{\LaTeX} distribution is required, too, for example TeX Live. Depending on your OS/platform, it can be in the form of one or several packages.

  2. Edit the rst files in doc/ directory using your favorite text editor - the ReST format is really simple, so nothing fancy is needed. Follow the existing files in doc/; for reference also check reStructuredText Primer, Sphinx Markup Constructs and docutils reStructuredText.

    • When adding a new Python module, add a corresponding documentation file into doc/src/sfepy/<path>, where <path> should reflect the location of the module in sfepy/.

    • Figures belong to doc/images; subdirectories can be used.

  3. (Re)generate the documentation (assuming GNU make is installed):

    cd doc
make html

  4. View it (substitute your favorite browser):

    firefox _build/html/index.html

How to Implement a New Term

Warning Implementing a new term usually involves C. As Cython is now supported by our build system, it should not be that difficult. Python-only terms are possible as well.

Note There is an experimental way (newly from version 2021.1) of implementing multi-linear terms that is much easier than what is described here, see Multi-linear Terms.

Notes on terminology

Term integrals are over domains of the cell or facet kinds. For meshes with elements of the topological dimension t \leq d, where d is the space dimension, cells have the topological t, while facets t-1. For example, in 3D meshes cell = volume, facet = surface, while in 2D cell = area, facet = curve.

Introduction

A term in SfePy usually corresponds to a single integral term in (weak) integral formulation of an equation. Both cell and facet integrals are supported. There are three types of arguments a term can have:

  • variables, i.e. the unknown, test or parameter variables declared by the variables keyword, see sec-problem-description-file,

  • materials, corresponding to material and other parameters (functions) that are known, declared by the materials keyword,

  • user data - anything, but user is responsible for passing them to the evaluation functions.

SfePy terms are subclasses of sfepy.terms.terms.Term. The purpose of a term is to implement a (vectorized) function that evaluates the term contribution to residual/matrix and/or evaluates the term integral in elements of the term region. Many such functions are currently implemented in C, but some terms are pure Python, vectorized using NumPy.

Evaluation modes

A term can support several evaluation modes, as described in Term Evaluation.

Basic attributes

A term class should inherit from sfepy.terms.terms.Term base class. The simplest possible term with cell integration and ‘weak’ evaluation mode needs to have the following attributes and methods:

  • docstring (not really required per se, but we require it);

  • name attribute - the name to be used in equations;

  • arg_types attribute - the types of arguments the term accepts;

  • integration attribute, optional - the kind of integral the term implements, one of ‘cell’ (the default, if not given), ‘facet’ or ‘facet_extra’;

  • function() static method - the assembling function;

  • get_fargs() method - the method that takes term arguments and converts them to arguments for function().

Argument types

The argument types can be (“[_*]” denotes an optional suffix):

  • ‘material[_*]’ for a material parameter, i.e. any function that can be can evaluated in quadrature points and that is not a variable;

  • ‘opt_material[_*]’ for an optional material parameter, that can be left out - there can be only one in a term and it must be the first argument;

  • ‘virtual’ for a virtual (test) variable (no value defined), ‘weak’ evaluation mode;

  • ‘state[_*]’ for state (unknown) variables (have value), ‘weak’ evaluation mode;

  • ‘parameter[_*]’ for parameter variables (have known value), any evaluation mode.

Only one ‘virtual’ variable is allowed in a term.

Integration kinds

The integration kinds have the following meaning:

  • ‘cell’ for cell integral over a region that contains elements; uses cell connectivity for assembling;

  • ‘facet’ for facet integral over a region that contains faces; uses facet connectivity for assembling;

  • ‘facet_extra’ for facet integral over a region that contains faces; uses cell connectivity for assembling - this is needed if full gradients of a variable are required on the boundary.

function()

The function() static method has always the following arguments:

out, *args

where out is the already preallocated output array (change it in place!) and *args are any other arguments the function requires. These function arguments have to be provided by the get_fargs() method. The function returns zero status on success, nonzero on failure.

The out array has shape (n_el, 1, n_row, n_col), where n_el is the number of elements and n_row, n_col are matrix dimensions of the value on a single element.

get_fargs()

The get_fargs() method has always the same structure of arguments:

  • positional arguments corresponding to arg_types attribute:

    • example for a typical weak term:

      • for:

        arg_types = ('material', 'virtual', 'state')

        the positional arguments are:

        material, virtual, state

  • keyword arguments common to all terms:

    mode=None, term_mode=None, diff_var=None, **kwargs

    here:

    • mode is the actual evaluation mode, default is ‘eval’;

    • term_mode is an optional term sub-mode influencing what the term should return (example: dw_tl_he_neohook term has ‘strain’ and ‘stress’ evaluation sub-modes);

    • diff_var is taken into account in the ‘weak’ evaluation mode. It is either None (residual mode) or a name of variable with respect to differentiate to (matrix mode);

    • **kwargs are any other arguments that the term supports.

The get_fargs() method returns arguments for function().

Additional attributes

These attributes are used mostly in connection with the tests/test_term_call_modes.py test for automatic testing of term calls.

  • arg_shapes attribute - the possible shapes of term arguments;

  • geometries attribute - the list of reference element geometries that the term supports;

  • mode attribute - the default evaluation mode.

Argument shapes

The argument shapes are specified using a dict of the following form:

arg_shapes = {'material' : 'D, D', 'virtual' : (1, 'state'),
              'state' : 1, 'parameter_1' : 1, 'parameter_2' : 1}

The keys are the argument types listed in the arg_types attribute, for example:

arg_types = (('material', 'virtual', 'state'),
             ('material', 'parameter_1', 'parameter_2'))

The values are the shapes containing either integers, or ‘D’ (for space dimension) or ‘S’ (symmetric storage size corresponding to the space dimension). For materials, the shape is a string ‘nr, nc’ or a single value, denoting a special-valued term, or None denoting an optional material that is left out. For state and parameter variables, the shape is a single value. For virtual variables, the shape is a tuple of a single shape value and a name of the corresponding state variable; the name can be None.

When several alternatives are possible, a list of dicts can be used. For convenience, only the shapes of arguments that change w.r.t. a previous dict need to be included, as the values of the other shapes are taken from the previous dict. For example, the following corresponds to a case, where an optional material has either the shape (1, 1) in each point, or is left out:

1arg_types = ('opt_material', 'parameter')
2arg_shapes = [{'opt_material' : '1, 1', 'parameter' : 1},
3              {'opt_material' : None}]

Geometries

The default that most terms use is a list of all the geometries:

geometries = ['2_3', '2_4', '3_4', '3_8']

In that case, the attribute needs not to be define explicitly.

Examples

Let us now discuss the implementation of a simple weak term dw_integrate defined as \int_{\cal{D}} c q, where c is a weight (material parameter) and q is a virtual variable. This term is implemented as follows:

 1class IntegrateOperatorTerm(Term):
 2    r"""
 3    Integral of a test function weighted by a scalar function
 4    :math:`c`.
 5
 6    :Definition:
 7
 8    .. math::
 9        \int_{\cal{D}} q \mbox{ or } \int_{\cal{D}} c q
10
11    :Arguments:
12        - material : :math:`c` (optional)
13        - virtual  : :math:`q`
14    """
15    name = 'dw_integrate'
16    arg_types = ('opt_material', 'virtual')
17    arg_shapes = [{'opt_material' : '1, 1', 'virtual' : (1, None)},
18                  {'opt_material' : None}]
19    integration = ('cell', 'facet')
20
21    @staticmethod
22    def function(out, material, bf, geo):
23        bf_t = nm.tile(bf.transpose((0, 1, 3, 2)), (out.shape[0], 1, 1, 1))
24        bf_t = nm.ascontiguousarray(bf_t)
25        if material is not None:
26            status = geo.integrate(out, material * bf_t)
27        else:
28            status = geo.integrate(out, bf_t)
29        return status
30
31    def get_fargs(self, material, virtual,
32                  mode=None, term_mode=None, diff_var=None, **kwargs):
33        assert_(virtual.n_components == 1)
34        geo, _ = self.get_mapping(virtual)
35
36        return material, geo.bf, geo

  • lines 2-14: the docstring - always write one!

  • line 15: the name of the term, that can be referred to in equations;

  • line 16: the argument types - here the term takes a single material parameter, and a virtual variable;

  • lines 17-18: the possible argument shapes

  • line 19: the integration mode is choosen according to a given domain

  • lines 21-29: the term function

    • its arguments are:

      • the output array out, already having the required shape,

      • the material coefficient (array) mat evaluated in physical quadrature points of elements of the term region,

      • a base function (array) bf evaluated in the quadrature points of a reference element and

      • a reference element (geometry) mapping geo.

    • line 23: transpose the base function and tile it so that is has the correct shape - it is repeated for each element;

    • line 24: ensure C contiguous order;

    • lines 25-28: perform numerical integration in C - geo.integrate() requires the C contiguous order;

    • line 29: return the status.

  • lines 31-36: prepare arguments for the function above:

    • line 33: verify that the variable is scalar, as our implementation does not support vectors;

    • line 34: get reference element mapping corresponding to the virtual variable;

    • line 36: return the arguments for the function.

A more complex term that involves an unknown variable and has two call modes, is dw_s_dot_mgrad_s, defined as \int_{\Omega} q \ul{y} \cdot \nabla p in the`’grad_state’` mode or \int_{\Omega} p \ul{y} \cdot \nabla q in the ‘grad_virtual’ mode, where \ul{y} is a vector material parameter, q is a virtual variable, and p is a state variable:

 1class ScalarDotMGradScalarTerm(Term):
 2    r"""
 3    Volume dot product of a scalar gradient dotted with a material vector
 4    with a scalar.
 5
 6    :Definition:
 7
 8    .. math::
 9        \int_{\Omega} q \ul{y} \cdot \nabla p \mbox{ , }
10        \int_{\Omega} p \ul{y} \cdot \nabla q
11
12    :Arguments 1:
13        - material : :math:`\ul{y}`
14        - virtual  : :math:`q`
15        - state    : :math:`p`
16
17    :Arguments 2:
18        - material : :math:`\ul{y}`
19        - state    : :math:`p`
20        - virtual  : :math:`q`
21    """
22    name = 'dw_s_dot_mgrad_s'
23    arg_types = (('material', 'virtual', 'state'),
24                 ('material', 'state', 'virtual'))
25    arg_shapes = [{'material' : 'D, 1',
26                   'virtual/grad_state' : (1, None),
27                   'state/grad_state' : 1,
28                   'virtual/grad_virtual' : (1, None),
29                   'state/grad_virtual' : 1}]
30    modes = ('grad_state', 'grad_virtual')
31
32    @staticmethod
33    def function(out, out_qp, geo, fmode):
34        status = geo.integrate(out, out_qp)
35        return status
36
37    def get_fargs(self, mat, var1, var2,
38                  mode=None, term_mode=None, diff_var=None, **kwargs):
39        vg1, _ = self.get_mapping(var1)
40        vg2, _ = self.get_mapping(var2)
41
42        if diff_var is None:
43            if self.mode == 'grad_state':
44                geo = vg1
45                bf_t = vg1.bf.transpose((0, 1, 3, 2))
46                val_qp = self.get(var2, 'grad')
47                out_qp = bf_t * dot_sequences(mat, val_qp, 'ATB')
48
49            else:
50                geo = vg2
51                val_qp = self.get(var1, 'val')
52                out_qp = dot_sequences(vg2.bfg, mat, 'ATB') * val_qp
53
54            fmode = 0
55
56        else:
57            if self.mode == 'grad_state':
58                geo = vg1
59                bf_t = vg1.bf.transpose((0, 1, 3, 2))
60                out_qp = bf_t * dot_sequences(mat, vg2.bfg, 'ATB')
61
62            else:
63                geo = vg2
64                out_qp = dot_sequences(vg2.bfg, mat, 'ATB') * vg1.bf
65
66            fmode = 1
67
68        return out_qp, geo, fmode

Only interesting differences with respect to the previous example will by discussed:

  • the argument types and shapes (lines 23-29) have to be specified for all the call modes (line 30)

  • the term function (lines 32-35) just integrates the element contributions, as all the other calculations are done by the get_fargs() function.

  • the get_fargs() function (lines 37-68) contains:

    • residual computation (lines 43-54) for both modes

    • matrix computation (lines 57-66) for both modes

Concluding remarks

This is just a very basic introduction to the topic of new term implementation. Do not hesitate to ask the SfePy mailing list, and look at the source code of the already implemented terms.

Multi-linear Terms

tentative documentation, the enriched einsum notation is still in flux

Multi-linear terms can be implemented simply by using the following enriched einsum notation:

The enriched einsum notation for defining multi-linear terms.

symbol

meaning

example

0

scalar

p

i

i-th vector component

u_i

i.j

gradient: derivative of i-th vector component w.r.t. j-th coordinate component

\pdiff{u_i}{x_j}

i:j

symmetric gradient

\frac{1}{2} (\pdiff{u_i}{x_j} + \pdiff{u_j}{x_i})

s(i:j)->I

vector storage of symmetric second order tensor, I is the vector component

Cauchy strain tensor e_{ij}(\ul{u})

The examples below present the new way of implementing the terms shown in the original Examples, using sfepy.terms.terms_multilinear.ETermBase.

Examples

  • de_integrate defined as \int_\Omega c q, where c is a weight (material parameter) and q is a virtual variable:

     1class EIntegrateOperatorTerm(ETermBase):
 2    r"""
 3    Volume and surface integral of a test function weighted by a scalar
 4    function :math:`c`.
 5
 6    :Definition:
 7
 8    .. math::
 9      \int_{\cal{D}} q \mbox{ or } \int_{\cal{D}} c q
10
11    :Arguments:
12        - material : :math:`c` (optional)
13        - virtual  : :math:`q`
14    """
15    name = 'de_integrate'
16    arg_types = ('opt_material', 'virtual')
17    arg_shapes = [{'opt_material' : '1, 1', 'virtual' : (1, None)},
18                  {'opt_material' : None}]
19
20    def get_function(self, mat, virtual, mode=None, term_mode=None,
21                     diff_var=None, **kwargs):
22        if mat is None:
23            fun = self.make_function(
24                '0', virtual, diff_var=diff_var,
25            )
26
27        else:
28            fun = self.make_function(
29                '00,0', mat, virtual, diff_var=diff_var,
30            )
31
32        return fun

  • de_s_dot_mgrad_s defined as \int_{\Omega} q \ul{y} \cdot \nabla p in the`’grad_state’` mode or \int_{\Omega} p \ul{y} \cdot \nabla q in the ‘grad_virtual’ mode, where \ul{y} is a vector material parameter, q is a virtual variable, and p is a state variable:

     1class EScalarDotMGradScalarTerm(ETermBase):
 2    r"""
 3    Volume dot product of a scalar gradient dotted with a material vector with
 4    a scalar.
 5
 6    :Definition:
 7
 8    .. math::
 9        \int_{\Omega} q \ul{y} \cdot \nabla p \mbox{ , }
10        \int_{\Omega} p \ul{y} \cdot \nabla q
11
12    :Arguments 1:
13        - material : :math:`\ul{y}`
14        - virtual  : :math:`q`
15        - state    : :math:`p`
16
17    :Arguments 2:
18        - material : :math:`\ul{y}`
19        - state    : :math:`p`
20        - virtual  : :math:`q`
21    """
22    name = 'de_s_dot_mgrad_s'
23    arg_types = (('material', 'virtual', 'state'),
24                 ('material', 'state', 'virtual'))
25    arg_shapes = [{'material' : 'D, 1',
26                   'virtual/grad_state' : (1, None),
27                   'state/grad_state' : 1,
28                   'virtual/grad_virtual' : (1, None),
29                   'state/grad_virtual' : 1}]
30    modes = ('grad_state', 'grad_virtual')
31
32    def get_function(self, mat, var1, var2, mode=None, term_mode=None,
33                     diff_var=None, **kwargs):
34        return self.make_function(
35            'i0,0,0.i', mat, var1, var2, diff_var=diff_var,
36        )

How To Make a Release

Module Index

sfepy package

sfepy.applications package

sfepy.base package

sfepy.discrete package

This package implements various PDE discretization schemes (FEM or IGA).

sfepy.discrete.common sub-package

Common lower-level code and parent classes for FEM and IGA.

sfepy.discrete.fem sub-package

sfepy.discrete.dg sub-package

sfepy.discrete.iga sub-package

sfepy.discrete.structural sub-package

sfepy.homogenization package

sfepy.linalg package

sfepy.mechanics package

sfepy.mesh package

sfepy.parallel package

sfepy.postprocess package

sfepy.solvers package

sfepy.terms package

Scripts

Tests

Tools