An FFT T‐matrix method for 3D microwave scattering solutions from random discrete scatterers

Abstract

An efficient method to solve the scattering by a cluster of randomly located discrete scatterers is described. The scatterers can have an arbitrary shape, and only their T matrices need be known. An iterative method is suggested to solve this problem. To expedite the matrix‐vector multiply, we first aggregate the random scattering centers of the scatterers into centers that reside on a regular array. Then, the FFT method is used to perform the matrix‐vector multiply in O(N log N) operations. This method can solve a problem with a large number of unknowns, involving thousands of discrete scatterers, on a workstation. © 1995 John Wiley & Sons, Inc.

Light Wave Propagation and Scattering Through Particles

“…Over the past few decades, some theories and numerical methods have been developed to study the light scattering by random discrete particles [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. In this section, we introduce a hybrid finite element-boundary integral-characteristic basis function method (FE-BI-CBFM) to simulate the light scattering by random discrete particles [49].…”

Fast algorithm for matrix–vector multiply of asymmetric multilevel block‐Toeplitz matrices in 3‐D scattering

“…computational complexity is O N log N , and the memory Figure 1. A T 2, 2, 2 matrix the type produced in 3 . the solution to the example in Section III would be similar, 3 Ž .…”

“…A T 2, 2, 2 matrix the type produced in 3 . the solution to the example in Section III would be similar, 3 Ž . Figure 1 Example of a A s T 2, 2, 2 asymmetric MBT matrix.…”

“…. The entries of Z constitute an MBT T N , N , N due to 3 x y z the translationally invariant Green's function kernel. The scattered electric field in the far field can be approximated using these induced dipole moments.…”

Symmetry Relations of the Translation Coefficients of the Spherical Scalar and Vector Multipole Fields

“…Their translation formulas [2][3][4][5][6][7][8][9], which express a spherical multipole field in one coordinate system in terms of the spherical multipole fields of another coordinate system that is related to the former by translation, have been a powerful analytic tool in many areas of electromagnetics. Early applications of the formulas include the plane-wave scattering from two metal spheres [10], which was later generalized to the scattering from many dielectric spheres in arbitrary configurations [11]; probe correction for spherical near-field scanning [12]; modeling of wave propagation through random discrete media [13]; extension of the Tmatrix technique for many scatterers [9] and its efficient numerical implementation using FFT [16,17]. As noted in [15], the cost of computing translation coefficients was found to be high and thus their recurrence relations [7,14,15] were derived in an attempt to contain this high cost.…”