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Implementation of Essential Boundary Conditions

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# 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.

## 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
examples/ example problem description files
meshes/ finite element mesh files in various formats shared by the examples
output/ default output directory for storing results of the examples
output-tests/ output directory for tests
script/ various small scripts (simple mesh generators, mesh format convertors etc.)
sfepy/ the source code
tests/ the tests run by run_tests.py
tmp/ directory for temporary files (generated)

New users/developers (after going through the Tutorial) should explore the 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 that implements all that simple.py script does)
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

mesh/ some utilities to interface with tetgen and triangle mesh generators
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.
optimize/ modules for shape optimization based on free-form deformation
physics/ small utilities for quantum physics (schroedinger.py)
postprocess/ Mayavi-based post-processing modules (postproc.py)
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

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

The fem/ 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 (see also Using IPython) to have the tab completion available. Moreover, all SfePy classes can be easily examined by printing them:

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 In [1]: from sfepy.discrete.fem import Mesh In [2]: mesh = Mesh.from_file('meshes/2d/rectangle_tri.mesh') sfepy: reading mesh [line2, tri3, quad4, tetra4, hexa8] (meshes/2d/rectangle_tri.mesh)... sfepy: ...done in 0.00 s In [3]: print mesh Mesh:meshes/2d/rectangle_tri cmesh: CMesh: n_coor: 258, dim 2, tdim: 2, n_el 454 descs: list: ['2_3'] dim: 2 dims: list: [2] io: None n_el: 454 n_nod: 258 name: meshes/2d/rectangle_tri nodal_bcs: 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. 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 or find current problems, issues, and suggestions of particular topics for additional development
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 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 web page. 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 and post comments to issues. It is, however, not needed to create a new issue.

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.

Our persisting all star top priority issues include:

• missing docstrings in many functions/classes/modules
• incomplete documentation
• lowering the barrier for new users
• e.g., through generation of additional tutorial material

So 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.

### Making changes¶

This step is simple, just keep in mind to use the latest development version of the code from the SfePy git repository page.

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 nice git patch than in another form.

Having said that, to download the latest snapshot, do either (with git):

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

or (without git):

Then make the changes as you wish, following our Coding style.

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.

### 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.

### Contributing changes¶

Even if you do not use git, try to follow the spirit of Notes on commits and patches

#### Without 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.

#### With git¶

Note: This section will get quickly get you started using git and github. For more in-depth reading about how these tools work with the SfePy source code and the general git development, read Working with SfePy source code, which was adapted from Matthew Brett’s excellent gitwash git tutorial.

With git there are some additional options for how to send changes to SfePy. Before listing them, let us describe a typical development session and the related git commands:

1. Either clone a fresh copy by:

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


or update your local repository:

 1 2 3 4 5 6 7 8 # look for changes at origin git fetch origin # difference between local and origin master branch git diff master origin/master # apply the changes to local master branch git pull origin master 
2. Introduce yourself to git and make (optionally) some handy aliases either in .gitconfig in your home directory (global setting for all your git projects), or directly in .git/config in the repository:

  1 2 3 4 5 6 7 8 9 10 11 12 13 [user] email = mail@mail.org name = Name Surname [color] ui = auto interactive = true [alias] ci = commit di = diff --color-words st = status co = checkout 
3. Change some file(s), and review the changes:

 1 2 3 4 5 # text diff git diff # use GUI to visualize of project history (all branches) gitk --all 
4. Create one or more commits:

 1 2 3 4 # schedule some of the changed files for the next commit git add file1 file2 ... # an editor will pop up where you should describe the commit git commit 
5. The commit(s) now reflect changes, but only in your local git repository. Then you must somehow allow others to see them. This can be done, for example, by sending a patch (or through the other option below). So create the patch(es):

# create patches for, e.g., the last two commits
git format-patch HEAD~2

6. Send the patch(es) to the SfePy mailing list or attach them to the corresponding issue at the Issues web page.

7. If the patches are fine, they will appear in the master repository. Then synchronize your repository with the master:

• either clone a fresh copy
• or use the fetch, pull, merge or rebase commands. This may require a deeper git-fu in case of conflicts. For beginners, it is advisable to clone always a fresh copy if they see a conflict.

There is another option than submitting patches, however, useful when you wish to get feedback on a larger set of changes. This option is to publish your repository using Github and let the other developers know about it - follow the instructions in Git for development of Working with SfePy source code.

#### 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”.

#### 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:

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

It seems visually better than:

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

When using in a docstring, use a raw string:

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

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 and numpydoc. 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 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¶

tentative documentation

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.

### Notes on terminology¶

Volume refers to the whole domain (in space of dimension ), while surface to a subdomain of dimension , for example a part of the domain boundary. So in 3D problems volume = volume, surface = surface, while in 2D volume = area, surface = curve.

### Introduction¶

A term in SfePy usually corresponds to a single integral term in (weak) integral formulation of an equation. Both volume and surface 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 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.

Terms come in two flavors:

• standard terms are subclasses of sfepy.terms.terms.Term
• new terms are subclasses of sfepy.terms.terms_new.NewTerm

As new terms are now not much more than a highly experimental proof of concept, we will focus on the standard terms here.

The purpose of a standard term class is to implement a (vectorized) function that assembles the term contribution to residual/matrix and/or evaluates the term integral in elements of the term region simultaneously. Most such functions are currently implemented in C, but some terms are pure Python, vectorized using NumPy. A term with a C function needs to be able to extract the real data from its arguments and then pass those data to the C function.

### 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 volume 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 ‘volume’ (the default, if not given), ‘surface’ or ‘surface_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:

• ‘volume’ for volume integral over a region that contains elements; uses volume element connectivity for assembling;
• ‘surface’ for surface integral over a region that contains faces; uses surface face connectivity for assembling;
• ‘surface_extra’ for surface integral over a region that contains faces; uses volume element 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:

 1 2 3 arg_types = ('opt_material', 'parameter') arg_shapes = [{'opt_material' : '1, 1', 'parameter' : 1}, {'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.

### Example¶

Let us now discuss the implementation of a simple weak term dw_volume_integrate defined as , where is a weight (material parameter) and is a virtual variable. This term is implemented as follows:

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 class IntegrateVolumeOperatorTerm(Term): r""" Volume integral of a test function weighted by a scalar function :math:c. :Definition: .. math:: \int_\Omega q \mbox{ or } \int_\Omega c q :Arguments: - material : :math:c (optional) - virtual : :math:q """ name = 'dw_volume_integrate' arg_types = ('opt_material', 'virtual') arg_shapes = [{'opt_material' : '1, 1', 'virtual' : (1, None)}, {'opt_material' : None}] @staticmethod def function(out, material, bf, geo): bf_t = nm.tile(bf.transpose((0, 1, 3, 2)), (out.shape[0], 1, 1, 1)) bf_t = nm.ascontiguousarray(bf_t) if material is not None: status = geo.integrate(out, material * bf_t) else: status = geo.integrate(out, bf_t) return status def get_fargs(self, material, virtual, mode=None, term_mode=None, diff_var=None, **kwargs): assert_(virtual.n_components == 1) geo, _ = self.get_mapping(virtual) 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
• lines 20-28: 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 22: transpose the base function and tile it so that is has the correct shape - it is repeated for each element;
• line 23: ensure C contiguous order;
• lines 24-27: perform numerical integration in C - geo.integrate() requires the C contiguous order;
• line 28: return the status.
• lines 30-35: prepare arguments for the function above:
• line 32: verify that the variable is scalar, as our implementation does not support vectors;
• line 33: get reference element mapping corresponding to the virtual variable;
• line 35: return the arguments for the function.

### 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.

## Working with SfePy source code¶

This section was adapted from Matthew Brett’s excellent gitwash git tutorial. It complements the above sections and details several aspects of working with Git and Github.

It can be updated by running:

$curl -O https://raw.github.com/matthew-brett/gitwash/master/gitwash_dumper.py$ python gitwash_dumper.py doc/dev SfePy --repo-name=sfepy --github-user=sfepy --project-url=http://sfepy.org --project-ml-url=http://groups.google.com/group/sfepy-devel


in the SfePy source directory. Do not forget to delete the section title in doc/dev/gitwash/index.rst, as it is already here.