A Comparison of Preconditioners for the Steklov–Poincaré Formulation of the Fluid-Structure Coupling in Hemodynamics

A Fluid–Structure Interaction (FSI) problem can be reinterpreted as a heterogeneous problem with two subdomains. It is possible to describe the coupled problem at the interface between the fluid and the structure, yielding a nonlinear Steklov–Poincaré problem. The linear system can be linearized by Newton iterations on the interface and the resulting linear problem can be solved by the preconditioned GMRES method. In this work we investigate the behavior of preconditioners of Neumann–Neumann and Dirichlet–Neumann type. We find that, in the context of hemodynamics, the Dirichlet– Neumann, i.e., using Dirichlet boundary conditions on the fluid side and Neumann on the structure side, outperforms the Neumann–Neumann method, except when a weighting is used such that it basically reduces to the Dirichlet–Neumann method.