Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects

Abstract

The fast multipole method (FMM) and multilevel fast multipole algorithm (MLFMA) are reviewed. The number of modes required, block-diagonal preconditioner, near singularity extraction, and the choice of initial guesses are discussed to apply the MLFMA to calculating electromagnetic scattering by large complex objects. Using these techniques, we can solve the problem of electromagnetic scattering by large complex three-dimensional (3-D) objects such as an aircraft (VFY218) on a small computer.

Geometry Based Preconditioner for Radiation Problems Involving Wire and Surface Basis Functions

“…Because of that, many MoM acceleration strategies based on iterative solutions have emerged to reduce the computational complexity. Among these acceleration techniques, it must be pointed out the Fast Multipole Method (FMM) [4] and its multilevel version, the Multilevel Fast Multipole Algorithm (MLFMA) [5][6][7][8], which are extensively used at present. Nevertheless, the FMM and, in general, other methods that tackle the electromagnetic analysis within the framework of iterative schemes usually meet with difficulties when dealing with radiation problems.…”

Fast Analysis of Electrically Large Radome in Millimeter Wave Band With Fast Multipole Acceleration

“…For the matrix-vector product with N unknowns, the two-level FMM reduces both the memory requirement and numerical complexity from O(N 2 ) to O(N 1.5 ) and the three-level FMM reduces it to O(N 4/3 ) [16][17][18][19]. By using the multilevel fast multipole method (MLFMM), the numerical complexity can be further reduced to O(N log N ) [21][22][23][24].…”

“…In (9), L is an infinite number. However, in numerical practice, L must be truncated with the finite number of modes and the relative error is depending on L with the following relationship [18,21]:…”

Higher Order Hierarchical Legendre Basis Functions Application to the Analysis of Scattering by Uniaxial Anisotropic Objects

“…Several techniques have been proposed to reduce the memory demands as well as the solution complexity of the conventional MoM. Fast integral equation solvers, such as the multilevel fast multiple method (MLFMM) [4,5], adaptive integral method (AIM) [6,7] and its close counterpart, the precorrected FFT (PC-FFT) [8,9], reach the solution complexity and memory requirement as O(N log(N )). However, when the scatter becomes electrically large, the number of unknowns becomes so large that even the fast integral equation solvers cannot solve it efficiently.…”