Sparse factorization of the three-dimensional integral equations using overlapped localizing LOGOS modes

It has recently been observed that local-global solution modes provide a useful framework for the development of fast, direct solutions of integral equation formulations of frequency-domain electromagnetic radiation and scattering problems. In particular, overlapped, localizing LOGOS (OL-LOGOS) modes have been observed to provide a fast direct solution procedure with approximately O(N) memory and O(NlogN) CPU costs for fixed-frequency discretizations of integral equations in two dimensions. In the following we demonstrate that the same factorization strategy can be used to develop similarly efficient factorizations of integral equations in three dimensions.