FIAT: enabling classical and modern macroelements
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914014728028160 |
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| author | Brubeck, Pablo D. Kirby, Robert C. |
| author_facet | Brubeck, Pablo D. Kirby, Robert C. |
| contents | Many classical and modern finite element spaces are derived by dividing each computational cell into finer pieces. Such \emph{macroelements} frequently enable the enforcement of mathematically desirable properties such as divergence-free conditions or $C^1$ continuity in a simpler or more efficient manner than elements without the subdivision. Although a few modern software projects provide one-off support for particular macroelements, a general approach facilitating broad-based support has, until now, been lacking. In this work, we describe a major addition to the FIAT project to support a wide range of different macroelements. These enhancements have been integrated into the Firedrake code stack. We provide numerical evaluation of the new macroelement facility. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_14599 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | FIAT: enabling classical and modern macroelements Brubeck, Pablo D. Kirby, Robert C. Numerical Analysis 65N30 G.4; G.1.8 Many classical and modern finite element spaces are derived by dividing each computational cell into finer pieces. Such \emph{macroelements} frequently enable the enforcement of mathematically desirable properties such as divergence-free conditions or $C^1$ continuity in a simpler or more efficient manner than elements without the subdivision. Although a few modern software projects provide one-off support for particular macroelements, a general approach facilitating broad-based support has, until now, been lacking. In this work, we describe a major addition to the FIAT project to support a wide range of different macroelements. These enhancements have been integrated into the Firedrake code stack. We provide numerical evaluation of the new macroelement facility. |
| title | FIAT: enabling classical and modern macroelements |
| topic | Numerical Analysis 65N30 G.4; G.1.8 |
| url | https://arxiv.org/abs/2501.14599 |