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.

翻译：我们提出了一种新的抽象方法，用于表示和求解基于有限元方法的多域问题。相较于先前的研究，该方法的进步在于实现了一个单一的高层抽象，能够在混合变分问题形式化框架下表示多域问题。我们在UFL和Firedrake中实现了这一新抽象，并通过求解四边形-三角形混合单元类型问题、六面体-四边形混合单元类型问题以及流固耦合基准问题，验证了实现的正确性。