  We present a monolithic parallel Newton-multigrid solver for nonlinear three
dimensional fluid-structure interactions in Arbitrary Lagrangian Eulerian
formulation. We start with a finite element discretization of the coupled
problem, based on a remapping of the Navier-Stokes equation onto a fixed
reference framework. The strongly coupled fluid-structure interaction problem
is discretized with finite elements in time and finite differences in time. The
resulting nonlinear and linear systems of equations are large and show a very
high condition number. We present a novel Newton approach that is based on two
essential ideas: First, a static condensation of solid deformation by
exploiting the velocity-deformation relation $d_t u = v$. Second, the Jacobian
of the fluid-structure interaction system is simplified by neglecting all
derivatives with respect to the ALE deformation, an approximation that has
shown to have little impact. The resulting system of equation decouples into a
joint momentum equation and into two separated equations for the deformation
fields in solid and fluid. Besides a reduction of the problem sizes, the
approximation has a positive effect on the conditioning of the systems such
that multigrid solvers with simple smoothers like a parallel Vanka-iteration
can be applied. We demonstrate the efficiency of the resulting solver
infrastructure on a well-studied 2d test-case and we also introduce a
challenging 3d problem. For 3d problems we achieve a substantial acceleration
as compared to established approaches found in literature.

Numerical Analysis