A monolithic multigrid solver for 3d fluid-structure interaction problems

In this paper, we propose a geometric multigrid method for fluid-structure interaction problems in ALE coordinates. We aim at complex three dimensional systems describing the coupled dynamics of an incompressible fluid with an elastic structure. The equations in ALE formulation are discretized with stabilized finite elements on adaptively refined meshes. The focus of this work is on the geometric multigrid method used to solve the linearized equations. Key is the construction of a smoothing operation based on a splitting of the problem into a fluid and structure part. Besides analyzing the multigrid method, we will demonstrate the efficiency of the resulting solver on a complex three dimensional benchmark problem