Two-Level Newton and Hybrid Schwarz Preconditioners for Fluid-Structure Interaction

We introduce and study numerically a two-level Schwarz preconditioner for Newton-Krylov methods for fluid-structure interaction, with special consideration of the application area of simulating blood flow. Our approach monolithically couples the fluid to the structure on both fine and coarse grids and in the subdomain solves, insuring that there is multiphysics coupling during all aspects of the algorithm. The fluid-structure system is discretized on unstructured nonnested meshes, with an overlapping additive domain decomposition on both coarse and fine levels and multiplicative Schwarz preconditioning between levels. We investigate the effect of different coarse discretization sizes, solver stopping criteria, and overlap size, and we demonstrate that the method is robust to physical parameters including the structure's Young's modulus and the timestep size. Finally, we show effective preconditioning of the complicated coupled system, with nearly perfect weak scaling to a thousand processors and millions of unknowns.