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arXiv · 2307.12455

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

Julian Roth·Martyna Soszyńska·Thomas Richter·Thomas Wick
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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.

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Julian Roth, Martyna Soszyńska, Thomas Richter, Thomas Wick. 2023-07-23. A monolithic space-time temporal multirate finite element framework for interface and volume coupled problems. https://arxiv.org/abs/2307.12455

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