A note on robust preconditioners for monolithic fluid-structure interaction systems of finite element equations
For computational scientists solving coupled fluid-structure interaction problems, this offers a preconditioning approach that handles highly varying densities, though the improvements are incremental over existing methods.
This work develops robust preconditioners for monolithic fluid-structure interaction systems, achieving efficient Krylov subspace solvers across a wide range of flow densities (water, blood, air). The preconditioner approximates the LDU factorization and uses algebraic multigrid for the Schur complement, demonstrating robustness without providing specific numerical gains.
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 $\hat{L}\hat{D}\hat{U}$, where $\hat{L}$, $\hat{D}$ and $\hat{U}$ 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.