Iterative solvers for coupled fluid-solid scattering

The multigrid method is used for coupled fluid-solid scattering discretized by linear finite elements. Numerical results show that using Krylov methods as smoothers allows coarser spaces than with standard smoothers, such as Jacobi and Gauss-Seidel. Block diagonal preconditioning for the 2×2 block diagonal matrix of the coupled system is also considered. Both multigrid and block diagonal preconditioned iterations fail to converge for frequencies when the scatterer is at resonance. It is shown how to transform the system into an equivalent one to avoid the resonance and to recover the convergence of the iterations.