A monolithic space-time temporal multirate finite element framework for interface and volume coupled problems

TL;DR

This paper introduces a novel monolithic space-time multirate finite element framework for coupled interface and volume problems, demonstrating its effectiveness through computational experiments on wave-heat and poro-elastic problems.

Contribution

It presents the first monolithic multirate approach using tensor-product Galerkin discretization for coupled problems, with detailed analysis and validation.

Findings

Framework performs well in convergence tests

Effective for wave-heat and poro-elastic problems

Validated on Mandel's benchmark and 3D footing problem

Abstract

In this work, we propose and computationally investigate a monolithic space-time multirate scheme for coupled problems. The novelty lies in the monolithic formulation of the multirate approach as this requires a careful design of the functional framework, corresponding discretization, and implementation. Our method of choice is a tensor-product Galerkin space-time discretization. The developments are carried out for both prototype interface- and volume coupled problems such as coupled wave-heat-problems and a displacement equation coupled to Darcy flow in a poro-elastic medium. The latter is applied to the well-known Mandel's benchmark and a three-dimensional footing problem. Detailed computational investigations and convergence analyses give evidence that our monolithic multirate framework performs well.