An abstraction for solving multi-domain problems using finite element methods
Mathematical Software
2025-12-09 v1 Numerical Analysis
Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2512.06146,
title = {An abstraction for solving multi-domain problems using finite element methods},
author = {Koki Sagiyama and Lawrence Mitchell and David A. Ham},
journal= {arXiv preprint arXiv:2512.06146},
year = {2025}
}