Monolithic matrix-free solver for fluid-structure interaction problems.
New method of solving time-dependent FSI problems using the Finite Element Method in ALE frame of reference together with an implementation that is able to scale up to thousands of CPUs. We derive the monolithic predictor-corrector time integration scheme for the problem involving interaction between incompressible hyper elastic solid and incompressible fluid. To ensure the constant volume of the solid we modify the mass conservation equation by introducing volumetric stabilization. The proposed algorithm consists of several sub-steps at each time step. Among them, the most time-consuming is the solution of the generalized Stokes problem with strongly variable coefficients. This has to be done one or two times per each time step, depending on the method's variant.