English

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}
}
R2 v1 2026-07-01T08:12:29.875Z