New trends in acceleration and parallelization techniques

Abstract

Rigorous solutions of large-scale radiation and scattering problems are permanently present among the goals of the scientific community dedicated to computational electromagnetics. Research aimed at solving complex electromagnetic problems that can involve large numbers of unknowns plays a relevant role in the development of many real-life applications. In this context, the fast multipole method (FMM) and the multilevel fast multipole algorithm (MLFMA) have been extensively used for accelerating iterative solutions of dense matrix systems resulting from the application of the method of moments (MoM) to problems formulated with surface integral equations (SIEs). The purpose of using these acceleration techniques is to extend the applicability of MoM, whose matrix storage requirement is O(N2 ), while the number of operations is O(N3 ) for direct solutions or O(N2 ) for iterative solutions, to larger problems. FMM and MLFMA reduce computational costs to O(N1.5 ) and 0(N log N), respectively.