A field-split preconditioning technique for fluid-structure interaction problems with applications in biomechanics

TL;DR

This paper introduces a new field-split preconditioning method for Krylov solvers to efficiently handle fluid-structure interaction problems in biomedical simulations, improving convergence in complex 2D and 3D cases.

Contribution

The paper proposes a novel field-split preconditioner based on physical variable-based splitting and additive Schwarz strategy for FSI linear systems, enhancing solver performance.

Findings

Effective in 2D and 3D biomedical FSI simulations

Outperforms pure domain decomposition preconditioners

Reduces computational time and improves convergence

Abstract

We present a novel preconditioning technique for Krylov subspace algorithms to solve fluid-structure interaction (FSI) linearized systems arising from finite element discretizations. An outer Krylov subspace solver preconditioned with a geometric multigrid (GMG) algorithm is used, where for the multigrid level sub-solvers, a field-split (FS) preconditioner is proposed. The block structure of the FS preconditioner is derived using the physical variables as splitting strategy. To solve the subsystems originated by the FS preconditioning, an additive Schwarz (AS) block strategy is employed. The proposed field-split preconditioner is tested on biomedical FSI applications. Both 2D and 3D simulations are carried out considering aneurysm and venous valve geometries. The performance of the FS preconditioner is compared with that of a second preconditioner of pure domain decomposition type.