Multiscale finite element calculations in Python using SfePy

SfePy (simple finite elements in Python) is a software for solving various kinds of problems described by partial differential equations in one, two, or three spatial dimensions by the finite element method. Its source code is mostly (85%) Python and relies on fast vectorized operations provided by...

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Published in	Advances in computational mathematics Vol. 45; no. 4; pp. 1897 - 1921
Main Authors	Cimrman, Robert, Lukeš, Vladimír, Rohan, Eduard
Format	Journal Article
Language	English
Published	New York Springer US 01.08.2019 Springer Nature B.V
Subjects	Application programming interface Computational mathematics Computational Mathematics and Numerical Analysis Computational Science and Engineering Conduction heating Conductive heat transfer Finite element method Mathematical and Computational Biology Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Partial differential equations Source code Visualization Finite element method 74S05 Piezoelasticity 35Qxx Multiscale simulations SfePy 65M60 65Y05 65N30 Python
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Abstract	SfePy (simple finite elements in Python) is a software for solving various kinds of problems described by partial differential equations in one, two, or three spatial dimensions by the finite element method. Its source code is mostly (85%) Python and relies on fast vectorized operations provided by the NumPy package. For a particular problem, two interfaces can be used: a declarative application programming interface (API), where problem description/definition files (Python modules) are used to define a calculation, and an imperative API, that can be used for interactive commands, or in scripts and libraries. After outlining the SfePy package development, the paper introduces its implementation, structure, and general features. The components for defining a partial differential equation are described using an example of a simple heat conduction problem. Specifically, the declarative API of SfePy is presented in the example. To illustrate one of SfePy’s main assets, the framework for implementing complex multiscale models based on the theory of homogenization, an example of a two-scale piezoelastic model is presented, showing both the mathematical description of the problem and the corresponding code.
AbstractList	SfePy (simple finite elements in Python) is a software for solving various kinds of problems described by partial differential equations in one, two, or three spatial dimensions by the finite element method. Its source code is mostly (85%) Python and relies on fast vectorized operations provided by the NumPy package. For a particular problem, two interfaces can be used: a declarative application programming interface (API), where problem description/definition files (Python modules) are used to define a calculation, and an imperative API, that can be used for interactive commands, or in scripts and libraries. After outlining the SfePy package development, the paper introduces its implementation, structure, and general features. The components for defining a partial differential equation are described using an example of a simple heat conduction problem. Specifically, the declarative API of SfePy is presented in the example. To illustrate one of SfePy’s main assets, the framework for implementing complex multiscale models based on the theory of homogenization, an example of a two-scale piezoelastic model is presented, showing both the mathematical description of the problem and the corresponding code.
Author	Lukeš, Vladimír Cimrman, Robert Rohan, Eduard
Author_xml	– sequence: 1 givenname: Robert surname: Cimrman fullname: Cimrman, Robert email: cimrman3@ntc.zcu.cz organization: New Technologies - Research Centre, University of West Bohemia – sequence: 2 givenname: Vladimír orcidid: 0000-0001-6579-1868 surname: Lukeš fullname: Lukeš, Vladimír organization: NTIS – New Technologies for the Information Society, Faculty of Applied Sciences, University of West Bohemia – sequence: 3 givenname: Eduard surname: Rohan fullname: Rohan, Eduard organization: NTIS – New Technologies for the Information Society, Faculty of Applied Sciences, University of West Bohemia
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Snippet	SfePy (simple finite elements in Python) is a software for solving various kinds of problems described by partial differential equations in one, two, or three...
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SubjectTerms	Application programming interface Computational mathematics Computational Mathematics and Numerical Analysis Computational Science and Engineering Conduction heating Conductive heat transfer Finite element method Mathematical and Computational Biology Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Partial differential equations Source code Visualization
Title	Multiscale finite element calculations in Python using SfePy
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