A multilevel fast multipole algorithm for electrically small composite structures

Abstract

ABSTRACT:A multi-tree scheme to apply the low-frequency multilevel fast multipole algorithm to composite structures is presented, so that O(N) CPU time and memory usage are obtained. The convenience of "plug and play" in electromagnetic simulation is illustrated in the scenario of contact-region modeling with an inconsistent mesh.

Efficient Solutions of Metamaterial Problems Using a Low-Frequency Multilevel Fast Multipole Algorithm

“…Alternatively, metamaterial problems can be solved efficiently via LF-MLFMA based on an explicit representation of radiated and incoming fields in terms of multipoles [17][18][19][20][21][22][23]. For level l = 1, 2, .…”

“…In this paper, we present fast and accurate solutions of metamaterial problems using a low-frequency MLFMA (LF-MLFMA) based on the multipole representation [17][18][19][20][21][22][23]. We show that, by combining LF-MLFMA with a robust preconditioner, such as the sparse-approximate-inverse (SAI) preconditioner [24,25], complicated metamaterial problems can be solved efficiently and accurately.…”

“…Stabilization of MLFMA for low-frequency applications has attracted the interest of many researchers, leading to development of diverse approaches to solve the low-frequency breakdown problem [12][13][14][15][16][17][18][19][20][21][22][23]. In one approach, spectral representation of the Green's function is used so that electromagnetic waves are divided into propagating and evanescent parts [12][13][14][15].…”

“…Unfortunately, the accuracy of the resulting implementation is not totally controllable, whereas error controllability is an essential requirement for highly-accurate computations. A third and more rigorous approach is based on the multipole representation of electromagnetic waves [17][18][19][20][21][22][23]. The Green's function is factorized with a multipole series, but the multipoles are not converted into plane waves for diagonalization.…”