We present a method for updating certain hierarchical factorizations for solving linear integral equations with elliptic kernels. In particular, given a factorization corresponding to some initial geometry or material parameters, we can locally perturb the geometry or coefficients and update the initial factorization to reflect this change with asymptotic complexity that is poly-logarithmic in the total number of unknowns and linear in the number of perturbed unknowns. We apply our method to the recursive skeletonization factorization and hierarchical interpolative factorization and demonstrate scaling results for a number of different two-dimensional (2D) problem setups.
['Victor Minden', 'Anil Damle', 'Kenneth L. Ho', 'Lexing Ying']
A technique for updating hierarchical skeletonization-based factorizations of integral operators