Multiple-precision arithmetic implementation of the multilevel fast multipole algorithm

Abstract

We propose and demonstrate a multiple-precision arithmetic (MPA) framework applied to the inherent hierarchical tree structure of the multilevel fast multipole algorithm (MLFMA), dubbed the MPA-MLFMA that provides an unconventional but elegant treatment to both the low-frequency breakdown (LFB) and the efficiency limitations of MLFMA for electrically large problems with fine geometrical details. We show that a distinct machine precision (MP) can be assigned to each level of the tree structure of MPA-MLFMA, which, in turn, enables controlled accuracy and efficiency over arbitrarily large frequency bandwidths. We present the capabilities of MPA-MLFMA over a wide range of broadband and multiscale scattering problems. We also discuss the implications of a multiple-precision framework implemented in software and hardware platforms.