Fast multipole method solution using parametric geometry

Abstract

The fast multipole method is used to solve the electromagnetic scattering from three‐dimensional conducting bodies of arbitrary shape. The electric field integral equation is discretized by the method of moments. Instead of directly computing the matrix‐vector multiplication, which needs N2 multiplications, this approach reduces the complexity to O(N1.5). © 1994 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] …”

“…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].…”

Fast multipole method for scattering from an arbitrary PEC target above or buried in a lossy half space

“…Further, there has been significant interest in the fast multipole method (FMM). The simplest two-level (single-stage) FMM [13], [14] has computational complexity and memory…”

“…The FMM clusters the MoM basis elements into groups [13], [14], and the interactions between distant groups ("far" interactions) are handled by exploiting features of the FMM spectral propagator [13], [14], discussed further below. "Near" interactions are handled in a manner analogous to a conventional MoM analysis [3], [5], [7].…”

“…Under this circumstance, each component of the dyadic Green's function can in general be represented in terms of a direct and reflected term [30], [31]. The direct term is handled as in the conventional free-space FMM [13], [14]. Further, the reflected term corresponds to radiation from the expansion function, reflection at the half-space interface, and subsequent propagation to the testing function.…”