VIE-FG-FFT for Analyzing EM Scattering from Inhomogeneous Nonmagnetic Dielectric Objects

Abstract

A new realization of the volume integral equation (VIE) in combination with the fast Fourier transform (FFT) is established by fitting Green's function (FG) onto the nodes of a uniform Cartesian grid for analyzing EM scattering from inhomogeneous nonmagnetic dielectric objects. The accuracy of the proposed method is the same as that of the P-FFT and higher than that of the AIM and the IE-FFT especially when increasing the grid spacing size. Besides, the preprocessing time of the proposed method is obviously less than that of the P-FFT for inhomogeneous nonmagnetic dielectric objects. Numerical examples are provided to demonstrate the accuracy and efficiency of the proposed method.

Fitting Green’s Function FFT Acceleration Applied to Anisotropic Dielectric Scattering Problems

“…For anisotropic media, matrix element expression adds one term − (3) , while adds two terms − (3) and (5) , compared with that in [11]. No matter which type of matrix elements, the value of (1) has the following basic law: (17)…”

“…Green's Function. The FG-FFT frame for the anisotropic media MoM model is similar to that in ordinary media [11].…”

“…In the above 6 formulas, there are three different integral regions: tetrahedral integral region ,± ( ) , ( ) , and triangular integral region [ ( ) ( ) ] , corresponding to their Gaussian points { ⃗ } ( ⃗ ), note that (5) contains four triangular surface integrals for anisotropic model, while in [11] for isotropic model, (5) contains only one triangular surface integral. Obviously, ⃗ (1) ( ) = ⃗ (1) ,+ + ⃗ (1) ,−…”

“…The third approach for improving efficiency is the VIE in combination with the Fast Fourier Transform (FFT). At present, alternative FFT-based accelerating methods include the VIE-AIM [7], the VIE-P-FFT [8,9], VIE-IE-FFT [10], and VIE-FG-FFT [11], which are simply called the FFT-based methods. The thought behind the IE-FFT is interpolating Green's function onto the nodes of a uniform Cartesian grid by Lagrange polynomials.…”

“…Through the previous studies of these fast algorithms, it has been known that the VIE-P-FFT and VIE-FG-FFT have the same higher accuracy than the VIE-AIM and VIE-IE-FFT, especially when increasing the Cartesian grid spacing size. Besides, from the study in [11], the VIE-FG-FFT preprocessing time is generally less than that of the VIE-P-FFT, which depends on inhomogeneous degree of the dielectric object. So, for general inhomogeneous anisotropic objects, the scheme of the FG-FFT is selected to do algorithm acceleration in this work.…”