We propose novel block preconditioners for the implicit-in-time Immersed Boundary Method. We iteratively solve the coupled Eulerian and Lagrangian linear system with preconditioners that use domain truncation for the Schur complement associated with the structural degrees of freedom. This approach is particularly useful for applications where the structure covers a small part of the fluid domain as it allows for a faster construction of the discrete operators involved in the numerical solution of the linear system. The reduction in the degrees of freedom in the preconditioning stage results in a speedup of each iteration of the Krylov subspace solver while preserving the robustness of the numerical computations. The preconditioners are implemented in a high-performance software package and we present numerical results for large-scale systems with up to 50 million degrees of freedom to demonstrate the scalability of our method.
Luhana et al. (Fri,) studied this question.