Matrix-Free Kernels and Preconditioning Techniques for Immersed Boundary Solvers
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We present preconditioning techniques that can be efficiently applied to the solution of linear systems arising from the finite element approach for the immersed boundary method. One of the crucial aspects related to the implementation of immersed methodologies is the interaction between different computational meshes. On top of that, a key difficulty arises in the memory-distributed setting due to the independent partitioning across processors of the background and immersed grid. To address this issue, we exploit efficient non-matching computational kernels provided by the deal.II Finite Element library. In addition, by leveraging its matrix-free infrastructure, we can reduce the memory footprint and provide off-the-shelf building blocks that can be readily employed during preconditioning. We validate the effectiveness of our approach and the robustness of our preconditioning strategy by performing several numerical experiments in two and three dimensions using immersed geometries of different complexity.