A Numerical Study on a Preconditioned GMRES Solver with Algebraic Multigrid Accelerations for the Fluid-Structure Interaction Problems on Hybrid Meshes

In this work, we propose a preconditioned GMRES solver for a Schur complement equation of the linearized fluid-structure interaction problem, with respect to the displacement unknowns only on the interface. The preconditioning for the Schur complement equation requires approximate solutions of the fluid and structure sub-problems with appropriate boundary conditions on the interface, in particular, a Robin condition for the fluid problem and a Neumann condition for the structure problem. Both sub-problems are spatially discretized by a finite element method on hybrid meshes and temporally discretized by implicit first-order methods. The discretized equations of both sub-problems are solved by special algebraic multigrid methods. The performance of this preconditioned GMRES solver is compared with that of a Newton based fluid-structure interaction solver. The convergence dependence on different parameters is studied by numerical experiments.