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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Veröffentlicht in:Advances in computational mathematics Jg. 45; H. 4; S. 1897 - 1921
Hauptverfasser: Cimrman, Robert, Lukeš, Vladimír, Rohan, Eduard
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.08.2019
Springer Nature B.V
Schlagworte:
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
ISSN:1019-7168, 1572-9044
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-019-09666-0