Fast direct (noniterative) solvers for integral-equation formulations of scattering problems

Abstract

A family of direct (noniterative) solvers with reduced computational complexity is proposed for solving problems involving resonant or near-resonant structures. Based on the recursive interaction matrix algorithm, the solvers exploit the aggregation concept of the recursive aggregate T-matrix algorithm to accelerate the solution. Direct algorithms are developed to compute the scattered field and the current coefficient, and invert the impedance matrix. Computational complexities of these algorithms are expressed in terms of the number of harmonics P required to express the scattered field of a larger scatterer made up of N scatterers. The exact P-N relation is determined by the geometry.