Robert C Kirby
Code generation for generally mapped finite elements
Kirby, Robert C; Mitchell, Lawrence
Authors
Lawrence Mitchell
Abstract
Many classical finite elements such as the Argyris and Bell elements have long been absent from high-level PDE software. Building on recent theoretical work, we describe how to implement very general finite-element transformations in FInAT and hence into the Firedrake finite-element system. Numerical results evaluate the new elements, comparing them to existing methods for classical problems. For a second-order model problem, we find that new elements give smooth solutions at a mild increase in cost over standard Lagrange elements. For fourth-order problems, however, the newly enabled methods significantly outperform interior penalty formulations. We also give some advanced use cases, solving the nonlinear Cahn-Hilliard equation and some biharmonic eigenvalue problems (including Chladni plates) using C1 discretizations.
Citation
Kirby, R. C., & Mitchell, L. (2019). Code generation for generally mapped finite elements. ACM Transactions on Mathematical Software, 45(4), Article 41. https://doi.org/10.1145/3361745
Journal Article Type | Article |
---|---|
Acceptance Date | Sep 9, 2019 |
Publication Date | Dec 31, 2019 |
Deposit Date | Aug 29, 2018 |
Publicly Available Date | Jan 21, 2020 |
Journal | ACM Transactions on Mathematical Software |
Print ISSN | 0098-3500 |
Electronic ISSN | 1557-7295 |
Publisher | Association for Computing Machinery (ACM) |
Peer Reviewed | Peer Reviewed |
Volume | 45 |
Issue | 4 |
Article Number | 41 |
DOI | https://doi.org/10.1145/3361745 |
Public URL | https://durham-repository.worktribe.com/output/1350477 |
Related Public URLs | https://arxiv.org/pdf/1808.05513.pdf |
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Copyright Statement
© 2019 Copyright held by the owner/author(s). This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in ACM transactions on mathematical software, https://doi.org/10.1145/3361745
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