A kernel-independent wideband nested equivalent source approximation

Abstract

We introduce a kernel-independent wideband nested equivalent source approximation method. The nested equivalent source approximation (NESA), proposed by these authors to solve low frequency problems with linear complexity, is extended here to electrically large multiscale structures. The low frequency algorithm is directly employed at the bottom levels of an Octree clustering; in the high frequency regime, the directional low rank property is exploited, yielding a nested directional algorithm (Wideband NESA-WNESA) with O(N log N) complexity. Numerical results demonstrate the validity of the proposed solver.