A unified family of FFT-based methods for dielectric scattering problems

Abstract

A unified family of FFT-based methods for dielectric scattering problems Abstract-Investigation is conducted on the computational efficiency of van den Berg's integrated-squared-error algorithm with different variational basis functions (VBFs) when applied to dielectric problems. Members in this family include the Matrix interpretation of the Spectral Iteration Technique (MSIT) and the well-known Conjugate Gradient FFT (CGFFT)-each arises from choosing an appropriate form of the VBF. A third choice which is based on a generalized Neumann series (GNS) expansion of the inverse of the defining integral operator is shown to give much superior performance than either the MSIT or the CGFFT. Tests performed on a variety of object shapes and dielectric materials indicate that the GNS is the most efficient among all three FFT-based methods.

A comparative study of the computation of near-field scattering from resonant dielectric/PEC scatterers

“…With such a mesh, the block matrices, G,, etc., in (5) are expanded to, GcTP etc in (6) and remain circulant matrices of level 3 [6] which is a requirement for the use of FFTs on the matrices. The current vectors in (5) are also extended over the expanded mesh by filling in the region outside the scatterer with zeros. Thus whole regions expanded versions of either the top or bottom row of (5), e.g.…”

Adapting the Normalized Cumulative Periodogram Parameter-Choice Method to the Tikhonov Regularization of 2-D/Tm Electromagnetic Inverse Scattering Using Born Iterative Method

“…This procedure continues until the appropriate termination conditions are satisfied (given below). The above forward solver can be accelerated using the Conjugate Gradient (CG) algorithm with the Fast Fourier Transform (FFT) technique for matrix-vector multiplications [39,40]. To speed up the multi-view forward scattering problem, it is also possible to use the marchingon-in-source-position technique to provide a better initial guess to the CG-FFT algorithm [18,41].…”

A comparison of two FFT‐based methods for dielectric scattering problems

“…where j(") denotes a direction vector (also called variational basis function in the case of the GNS) to guide the unknown current vector to its desired solution 1 [2]. This is the major cost to any FFT-based method, and any further convolutional product will increase the computational time of the overall solution.…”

“…This article is concerned with the comparison of two FFT-based methods for solving dielectric scattering problems. The first one is associated with van den Berg's integratedsquared-error algorithm [4], where the variational basis function is chosen in a way that makes use of the generalized Neumann series (GNS) of the inverse of the defining operator [2]. The second one is the biconjugate-gradient FFT (Bi-CGFFT) method for symmetric indefinite systems [ S , 61.…”

“…The computational efficiency of the GNS when applied to dielectric problems compared to the other two members of van den Berg's algorithm has recently been demonstrated in [2]. For the Bi-CGFFT, its applicability to an infinitesimally thin conducting plate and comparison with the conjugate gradient FFT method are discussed in [6].…”