GMRES acceleration of subiteration for fluid-structure interactions

The numerical solution of fluid-structure interaction problems is of great relevance in many disciplines of engineering and science.Monolithic solution methods for fluid-structure interaction typically employ subiteration, i.e., multiple fluidstructure iterations. Although for certain problems the subiteration method is an excellent solver, for other problems it converges only slowly or even diverges.In this paper, we analyze the convergence behaviour of the subiteration method and investigate the application of under-relaxation and GMRES acceleration in order to improve its convergence behaviour. The Krylov acceleration constructs the search directions from available intermediate solution vectors already calculated in the subiterations. Therefore our proposed strategy is cheap and easily implemented in existing codes which use subiteration as a solver. The subiteration method can then be considered as a preconditioner to the Krylov subspace method. Numerical results for a model problem show that convergence difficulties are nicely mitigated by under-relaxation and GMRES acceleration, which demonstrates that our proposed strategy is capable to render the subiteration method more robust and efficient.