Efficient Solution of Integral Equations in a Localizing Basis

Abstract

A sparse direct solution algorithm is reported for discrete representations of boundary integral operators. The algorithm relies on an expansion of the unknown surface currents in a numerically determined basis of functions that are simultaneously localized to small regions on a larger target while also satisfying global boundary conditions. It is shown that the QR factorization of the impedance matrix is sparse in this basis at low to moderate frequencies.