A Note on Robust Preconditioners for Monolithic Fluid-structure Interaction Systems of Finite Element Equations

In this note, we consider preconditioned Krylov subspace methods for discrete fluid-structure interaction problems with a nonlinear hyperelastic material model and covering a large range of flows, e.g, water, blood, and air with highly varying density. Based on the complete LDU factorization of the coupled system matrix, the preconditioner is constructed in form of L̂D̂Û , where L̂, D̂ and Û are proper approximations to L, D and U , respectively. The inverse of the corresponding Schur complement is approximated by applying one cycle of a special class of algebraic multigrid methods to the perturbed fluid sub-problem, that is obtained by modifying corresponding entries in the original fluid matrix with an explicitly constructed approximation of the exact perturbation coming from the sparse matrix-matrix multiplications.