Parallel Skeletonization for Integral Equations in Evolving Multiply-Connected Domains

This paper presents a general method for applying hierarchical matrix skeletonization factorizations to the numerical solution of boundary integral equations with possibly rank-deficient operators. Rank-deficient operators arise in approaches elliptic partial differential multiple components, such as case vesicles viscous fluid flow. Our generalized factorization retains locality property afforded by “proxy point method,” and allows parallelized implementation where different processors work on parts simultaneously. Further, when undergoes local geometric perturbations (such movement an interior hole), can be recomputed efficiently respect number modified discretization nodes. We present application that leverages parallel updates shape optimization regime.