Institute of Fundamental Technological Research

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.

arbitrary Lagrangian-Eulerian, finite element method, fluid-structure interaction, geometric multigrid, matrix-free method, monolithic scheme

In this paper we present a matrix-free multilevel solver for the generalized Stokes problem with discontinuous viscosity. The algorithm is based on the FGMRES iteration preconditioned with a block-smoothed multigrid method. Numerical experiments on unstructured grids indicate that for a broad range of smoother parameters, the convergence speed is only weakly dependent on both the number of unknowns and the jumps of the viscosity coefficient.

Stokes problem, Discontinuous coefficients, Multigrid, Matrix-free, Parallel computing