An improved pulse-basis conjugate gradient FFT method for the thin conducting plate problem

Tran, Trung-Viet; McCowen, A.

doi:10.1109/8.214609

Cited by 11 publications

(10 citation statements)

References 18 publications

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“…The theoretical development of the GNS and biconjugate gradient FFT method for symmetric systems was given in [21 and [6]. Specifically, both methods are designed to solve for a first-kind integral equation for the form…”

Section: Review Of the Gns And Bi-cgfftmentioning

confidence: 99%

“…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]. Its application to dielectric scattering problems and its susceptibility to nonconvergence behavior have not, however, been hitherto published in the literature.…”

Section: Introductionmentioning

confidence: 99%

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

Tran

McCowen

1995

Micro & Optical Tech Letters

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The performance of two FFT‐based methods for solving dielectric scattering problems is investigated. The first method is associated with van den Berg's integrated‐squared‐error algorithm, where the variational basis function is based on a generalized Neumann series (GNS) expansion of the inverse of the defining integral operator. The second method is the biconjugate‐gradient FFT (Bi‐CGFFT) for symmetric indefinite systems. Both methods are applied to a variety of dielectric problems encompassing both homogeneous and inhomogeneous material compositions in twoand three‐dimensional spaces. Particular emphasis is placed on the identification of the class of problems that yield nonconvergence for the Bi‐CGFFT and the alleviation of this undesirable behavior.

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Section: Review Of the Gns And Bi-cgfftmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Tran

McCowen

1995

Micro & Optical Tech Letters

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“…An example of such case is the computation of electromagnetic scattering from an infinitesimally thin conducting plate [28], where both the MSIT and the GNS fail to converge; the only member of van den Berg's family that gives a convergence result is the CGFFT. The efficiency of the GNS for penetrable bodies, on the other hand, as has been convincingly demonstrated in this paper, leaves little doubt as to its applicability for any dielectric problems of interest.…”

Section: Three-dimensional Problemmentioning

confidence: 99%

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

Tran

McCowen

1994

Journal of Electromagnetic Waves and Applications

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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.

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“…One method directly discretized the integral equation by use of the moment method [21][22][23]. Another type of method is to first use Fourier transform to deal with the spatial derivation of the grad-div operation of the hyper-singular integral equation, and then discretize the integral equation in the spectral Fourier domain.…”

Section: Introductionmentioning

confidence: 99%

“…This method is called (CG-FFT [24][25][26][27][28]. In all of these approaches, different types of basis functions have been chosen: [21][22][23][24][25]27] which have adopted the pulse basis for both expansion and testing functions, where as [26,28] adopted the rooftop functions as expansion and testing functions which can yield more accurate results at an increased computational costs. This paper focuses on analyzing the scattering from perfectly conducting plates by AMMM.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Scattering from Perfectly Conducting Plates by the Use of AMMM

Sarkar

1999

PIER

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An improved pulse-basis conjugate gradient FFT method for the thin conducting plate problem

Cited by 11 publications

References 18 publications

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

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

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

Analysis of Scattering from Perfectly Conducting Plates by the Use of AMMM

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