Existence of ℋ-matrix approximants to the inverses of BEM matrices: The simple-layer operator

We consider the question of approximating the inverse W = V of the Galerkin stiffness matrix V obtained by discretizing the simple-layer operator V with piecewise constant functions. The block partitioning of W is assumed to satisfy any of the standard admissibility criteria that are employed in connection with clustering algorithms to approximate the discrete BEM operator V. We show that W can be approximated by blockwise low-rank matrices such that the error decays exponentially in the block rank employed. Similar exponential approximability results are shown for the Cholesky factorization of V.