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Automated Generation and Symbolic Manipulation of Tensor Product Finite Elements

McRae, A.T.T.; Bercea, G.-T.; Mitchell, L.; Ham, D.A.; Cotter, C.J.

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Authors

A.T.T. McRae

G.-T. Bercea

L. Mitchell

D.A. Ham

C.J. Cotter



Abstract

We describe and implement a symbolic algebra for scalar and vector-valued finite elements, enabling the computer generation of elements with tensor product structure on quadrilateral, hexahedral, and triangular prismatic cells. The algebra is implemented as an extension to the domain-specific language UFL, the Unified Form Language. This allows users to construct many finite element spaces beyond those supported by existing software packages. We have made corresponding extensions to FIAT, the FInite element Automatic Tabulator, to enable numerical tabulation of such spaces. This tabulation is consequently used during the automatic generation of low-level code that carries out local assembly operations, within the wider context of solving finite element problems posed over such function spaces. We have done this work within the code-generation pipeline of the software package Firedrake; we make use of the full Firedrake package to present numerical examples.

Citation

McRae, A., Bercea, G., Mitchell, L., Ham, D., & Cotter, C. (2016). Automated Generation and Symbolic Manipulation of Tensor Product Finite Elements. SIAM Journal on Scientific Computing, 38(5), S25-S47. https://doi.org/10.1137/15m1021167

Journal Article Type Article
Acceptance Date Mar 24, 2016
Online Publication Date Oct 27, 2016
Publication Date Oct 27, 2016
Deposit Date Aug 1, 2018
Publicly Available Date Mar 29, 2024
Journal SIAM Journal on Scientific Computing
Print ISSN 1064-8275
Electronic ISSN 1095-7197
Publisher Society for Industrial and Applied Mathematics
Peer Reviewed Peer Reviewed
Volume 38
Issue 5
Pages S25-S47
DOI https://doi.org/10.1137/15m1021167
Related Public URLs https://arxiv.org/pdf/1411.2940.pdf

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