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In this paper we study a monolithic Newton-Krylov solver with exact Jacobianfor the solution of incompressible FSI problems. A main focus of this work ison the use of geometric multigrid preconditioners with modified Richardsonsmoothers preconditioned by an additive Schwarz algorithm. The definition ofthe subdomains in the Schwarz smoother is driven by the natural splittingbetween fluid and solid. The monolithic approach guarantees the automaticsatisfaction of the stress balance and the kinematic conditions across thefluid-solid interface. The enforcement of the incompressibility conditions bothfor the fluid and for the solid parts is taken care of by using inf-sup stablefinite element pairs without stabilization terms. A suitable ArbitraryLagrangian Eulerian (ALE) operator is chosen in order to avoid meshentanglement while solving for large displacements of the moving fluid domain.Numerical results of two and three-dimensional benchmark tests with Newtonianfluids and nonlinear hyperelastic solids show a robust performance of our fullyincompressible solver especially for the more challengingdirect-to-steady-state problems.

A monolithic ALE Newton-Krylov solver with Multigrid-Richardson-Schwarz preconditioning for incompressible Fluid Structure Interaction