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

authored by

Julian Roth, Martyna Soszyńska, Thomas Richter, Thomas Wick

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.

Organisation(s)

Institute of Applied Mathematics
PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines

External Organisation(s)

Université Paris-Saclay
Otto-von-Guericke University Magdeburg

Type

Article

Journal

Journal of Computational and Applied Mathematics

Volume

446

Pages

115831

ISSN

0771-050X

Publication date

15.08.2024

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Computational Mathematics, Applied Mathematics

Electronic version(s)

https://doi.org/10.48550/arXiv.2307.12455 (Access: Open)
https://doi.org/10.1016/j.cam.2024.115831 (Access: Open)