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.

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.-T., 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: Aug 2, 2018
• 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
• Public URL: https://durham-repository.worktribe.com/output/1324868
• Related Public URLs: https://arxiv.org/pdf/1411.2940.pdf