A hierarchical multi-level fast multipole method for wideband multiscale electromagnetic wave scattering from non-penetrable targets in R3

For a variety of multiscale electromagnetic (EM) problems, mesh densities that are more than sufficient for the frequency of interest have to be adopted in order to maintain the integrity of multiscale geometrical features. The adoption of the overly fine mesh, or locally overly fine mesh, would render the multi-level fast multiple method (MLFMM) inefficient during the matrix-vector multiplication (MVP), both in terms of CPU time and memory consumption. Similar issue occurs also in wideband analyses. In this paper, we proposed a hierarchical multi-level fast multipole method (H-MLFMM) based on the skeletonalization technique to address effectively the EM scattering from targets with multiscale features. Numerical examples demonstrate the accuracy and applicability of the H-MLFMM algorithm.