Formulation and analysis of a Schur complement method for fluid-structure interaction

TL;DR

This paper develops a strongly coupled, non-iterative partitioned method for fluid-structure interaction based on a Schur complement approach, ensuring well-posedness and demonstrating promising numerical performance.

Contribution

It introduces a novel Schur complement-based partitioned scheme for FSI that is non-iterative and well-posed, with analysis and initial numerical validation.

Findings

Method achieves expected convergence rates

Schur complement system effectively decouples fluid and structure

Condition number bounds inform stability analysis

Abstract

This work presents a strongly coupled partitioned method for fluid-structure interaction (FSI) problems based on a monolithic formulation of the system which employs a Lagrange multiplier. We prove that both the semi-discrete and fully discrete formulations are well-posed. To derive a partitioned scheme, a Schur complement equation, which implicitly expresses the Lagrange multiplier and the fluid pressure in terms of the fluid velocity and structural displacement, is constructed based on the monolithic FSI system. Solving the Schur complement system at each time step allows for the decoupling of the fluid and structure subproblems, making the method non-iterative between subdomains. We investigate bounds for the condition number of the Schur complement matrix and present initial numerical results to demonstrate the performance of our approach, which attains the expected convergence rates.