Well-posedness and Robust Preconditioners for the Discretized Fluid-Structure Interaction Systems

TL;DR

This paper develops robust preconditioners for discretized fluid-structure interaction systems, ensuring well-posedness and efficiency in solving the resulting saddle point problems.

Contribution

It introduces a family of preconditioners based on uniform well-posedness proofs for ALE discretized FSI models, enhancing computational robustness.

Findings

Preconditioners demonstrate robustness in numerical tests.

Uniform well-posedness established for discretized systems.

Preconditioners improve solver efficiency.

Abstract

In this paper we develop a family of preconditioners for the linear algebraic systems arising from the arbitrary Lagrangian-Eulerian discretization of some fluid-structure interaction models. After the time discretization, we formulate the fluid-structure interaction equations as saddle point problems and prove the uniform well-posedness. Then we discretize the space dimension by finite element methods and prove their uniform well-posedness by two different approaches under appropriate assumptions. The uniform well-posedness makes it possible to design robust preconditioners for the discretized fluid-structure interaction systems. Numerical examples are presented to show the robustness and efficiency of these preconditioners.