Multilevel fast‐multipole algorithm for solving combined field integral equations of electromagnetic scattering

Abstract

The fast multipole method (FMM) has been implemented to speed up the matrix‐vector multiply when an iterative method is used to solve the combined field integral equation (CFIE). FMM reduces the complexity from O(N2) to O(N1.5). With a multilevel fast multipole algorithm (MLFMA), it is further reduced to O(N log N). A 110, 592‐unknown problem can be solved within 24 h on a SUN Sparc 10. © 1995 John Wiley & Sons, Inc.

Multilevel Fast Multipole Algorithm for Radiation Characteristics of Shipborne Antennas Above Seawater

“…While the dyadic ∆Ḡ Aii needs some further investigation (see below), the free-space FMM [12,13] or MLFMA [14] can be applied to the "direct" term, with only minor changes due to the (in general) lossy background. The free-space FMM and MLFMA are based on the addition theorem [12], leading to the (propagating) plane wave representation [12] …”

“…Using the expansion (4), the elements of the far interaction impedance matrix (i.e., for R m m sufficiently large) in the context of a free-space scattering problem can be written as [14] …”

“…In [9][10][11], Geng and colleagues developed an approximate means of handling the dyadic half-space Green's function, with application to the fast multipole method (FMM) and the multilevel fast multipole algorithm (MLFMA), which were originally developed for targets in free space [12][13][14][15][16][17][18][19][20][21][22]. In their works, the near MLFMA terms are evaluated via the use of the exact dyadic Green's function, the latter evaluated efficiently via the complex-image technique [23].…”

Mlfma-FFT Parallel Algorithm for the Solution of Large-Scale Problems in Electromagnetics

“…Consequently, as the capacity for solving large problems of hundreds of millions of unknowns grows, the electromagnetic numerical solvers and industrial necessities get closer. For all these reasons, in last years the well-known Method of Moments [1] made way for acceleration techniques as the Fast Multipole Method (FMM) [2] and its multilevel version, the MLFMA [3,4]. In fact, the attention of many recent studies is concentrated on the improvement of the MLFMA parallelization over shared, distributed and mixed memory computers [5][6][7][8][9][10][11][12][13][14][15].…”

A Stable Integral Equation Solver for Electromagnetic Scattering by Large Scatterers With Concave Surface

“…Fast Multiple Method (FMM) is thought of as a very robust numerical approach in dealing with electrically large problems [4][5][6][7][8][9]. The FMM can solve a matrix equation with 20 million unknowns on a common workstation [7].…”