SfePy (Simple finite elements in Python)

SfePy¹ is a software for solving systems of coupled partial differential equations (PDEs) by the finite element method in 1D, 2D and 3D. It can be viewed both as black-box PDE solver, and as a Python package which can be used for building custom applications. The word "simple" means that complex FEM problems can be coded very easily and rapidly. Its source code can be found on github².

SfePy is based primarily on NumPy³ and SciPy⁴. See the INSTALL file for installation instructions or refer to⁵.

• License: New BSD License, see the LICENSE file.
• Authors: Robert Cimrman and Contributors, see the AUTHORS file.

How to start

SfePy uses so called "problem definition files" (also referred to as "input files" or "problem description files"") that describe the partial differential equations (PDEs), boundary conditions, function spaces and other ingredients of the finite element (FE) formulation of a PDE-related problem, see⁶. The PDEs are given in weak formulation as usual in the FE context, see⁷, where each equation is composed of one or more terms. To see which terms are available consult doc/sfepy_manual.pdf, or see them online⁸.

In order to solve a problem, a problem description file has to be created. There is also an interactive solution support for advanced users⁹. When starting to solve a new problem, it is best to have a look at example problem definition files in the sfepy/examples/ directory - copy the one that is similar to the problem at hand, and modify it.

While a problem definition file describes a mathematical problem, it does not contain a discretized solution domain (a FE mesh). The FE mesh must be provided in another file in one of the supported formats, notably the legacy VTK format ¹⁰. SfePy does not provide meshing tools, but it can use a number of standard formats. The results are almost exclusively stored in legacy VTK files, or custom HDF5 files. Many standard open-source tools can be used to display the VTK files, namely paraview¹¹ or pyvista¹². The latter is supported directly within SfePy.

Once an input file and a corresponding mesh file are prepared, the solution of the problem can be sought, see the documentation.

References

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1. https://sfepy.org - main SfePy development site (releases, mailing lists, wiki, issue tracking, downloads, documentation, examples)↩

2. https://github.com/sfepy - master git repository↩

3. http://numpy.org↩

4. http://scipy.org↩

5. https://sfepy.org - main SfePy development site (releases, mailing lists, wiki, issue tracking, downloads, documentation, examples)↩

6. https://sfepy.org - main SfePy development site (releases, mailing lists, wiki, issue tracking, downloads, documentation, examples)↩

7. http://en.wikipedia.org/wiki/Weak_formulation↩

8. https://docs.sfepy.org/doc/terms_overview.html↩

9. https://docs.sfepy.org/doc/tutorial.html#interactive-example-linear-elasticity↩

10. http://www.vtk.org/VTK/img/file-formats.pdf↩

11. http://paraview.org/↩

12. https://docs.pyvista.org/↩