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arXiv · 2501.14599

FIAT: enabling classical and modern macroelements

Pablo D. Brubeck·Robert C. Kirby
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Abstract

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.

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Pablo D. Brubeck, Robert C. Kirby. 2025-01-24. FIAT: enabling classical and modern macroelements. https://arxiv.org/abs/2501.14599

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