An abstraction for solving multi-domain problems using finite element methods
Koki Sagiyama, Lawrence Mitchell, David A. Ham
TL;DR
This paper presents a new high-level abstraction for multi-domain finite element problems, implemented in UFL and Firedrake, enabling efficient solutions of complex coupled problems.
Contribution
It introduces a unified abstraction for multi-domain problems in the mixed variational formalism, advancing previous finite element frameworks.
Findings
Successfully implemented in UFL and Firedrake.
Validated on quad-triangle and hex-quad mixed problems.
Demonstrated effectiveness on fluid-structure interaction benchmark.
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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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Matrix Theory and Algorithms · Advanced Mathematical Modeling in Engineering