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arXiv · 2512.06146

An abstraction for solving multi-domain problems using finite element methods

Koki Sagiyama·Lawrence Mitchell·David A. Ham
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Abstract

We introduce a new abstraction for the representation and solution of multi-domain problems using finite element methods. This is an advance over previous work in that it achieves a single higher-level abstraction that represents multi-domain problems in the mixed variational problem formalism. We implemented our new abstraction in UFL and Firedrake, and validated our implementations solving a quad-triangle mixed-cell-type problem, a hex-quad mixed-cell-type problem, and a fluid-structure interaction benchmark problem.

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Koki Sagiyama, Lawrence Mitchell, David A. Ham. 2025-12-05. An abstraction for solving multi-domain problems using finite element methods. https://arxiv.org/abs/2512.06146

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