Robust preconditioning of monolithically coupled multiphysics problems

TL;DR

This paper introduces a robust preconditioning framework for coupled multiphysics problems, leveraging fractional Laplacian operators to improve solution stability and efficiency across interface-dependent systems.

Contribution

The paper presents a novel preconditioning approach using fractional Laplacians applicable to general coupled multiphysics problems, validated on Darcy-Stokes and fluid-structure interaction models.

Findings

Effective preconditioning improves convergence in coupled systems.

Framework is applicable to Darcy-Stokes and fluid-structure interaction problems.

Numerical results confirm robustness and efficiency of the method.

Abstract

In many applications, one wants to model physical systems consisting of two different physical processes in two different domains that are coupled across a common interface. A crucial challenge is then that the solutions of the two different domains often depend critically on the interaction at the interface and therefore the problem cannot be easily decoupled into its subproblems. Here, we present a framework for finding robust preconditioners for a fairly general class of such problems by exploiting operators representing fractional and weighted Laplacians at the interface. Furthermore, we show feasibility of the framework for two common multiphysics problems; namely the Darcy-Stokes problem and a fluid--structure interaction problem. Numerical experiments that demonstrate the effectiveness of the approach are included.