Exploiting high‐contrast Stokes preconditioners to efficiently solve incompressible fluid–structure interaction problems

In this work, we develop a new algorithm to solve large-scale incompressible time-dependent fluid–structure interaction problems using a matrix-free finite element method in arbitrary Lagrangian–Eulerian frame of reference. We derive a semi-implicit time integration scheme which improves the geometry-convective explicit scheme for problems involving the interaction between incompressible hyperelastic solids and incompressible fluids. The proposed algorithm relies on the reformulation of the time-discrete problem as a generalized Stokes problem with strongly variable coefficients, for which optimal preconditioners have recently been developed. The resulting algorithm is scalable, optimal, and robust: we test our implementation on model problems that mimic classical Turek–Hron benchmarks in two and three dimensions, and investigate timing and scalability results.