Three‐dimensional weak‐form conjugate‐ and biconjugate‐gradient FFT methods for volume integral equations

Zhang, Z. Q.; Liu, Q. H.

doi:10.1002/mop.1176.abs

Cited by 19 publications

(44 citation statements)

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“…Defined as in [21,22], d uvw q and a uvw q are the value of the q component of the electric flux density and the vector potential at the center of the rooftop functions. With this choice for the basis functions, the normal component of D is continuous across all facets of the grid, as required by the boundary conditions.…”

Section: Weak Form Testing and Expansion Proceduresmentioning

confidence: 99%

“…The vector potential A is a spatial convolution of the free space Green's function G and the contrast source J over the domain of interest. As in [21,22], a weak form of the integral equation for the relevant unknown quantity is obtained by testing it with appropriate testing functions. Then the vector potential is expanded in a sequence of the appropriate expansion functions and the grad-div operator is integrated analytically over the scattering object domain only.…”

Section: Weak Form Testing and Expansion Proceduresmentioning

confidence: 99%

“…However, NUFFT algorithm is difficult to be directly applied for the case of two-dimensional problems with transverse electric wave incidence and three-dimensional problems due to the existing of the higher order singularity of the dyad Green's function in the integral equations. In this article, we adopt the idea of the weak-form integral equations introduced in [21,22], which leads to a weaker singularity in the Green's function, to overcome this restriction. Both FFT and NUFFT algorithms reduce the CPU time to O(N log 2 N ) and computer memory to O(N ) [23][24][25][26], much smaller than O(N 2 ) by the MoM.…”

Section: Introductionmentioning

confidence: 99%

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Weak Form Nonuniform Fast Fourier Transform Method for Solving Volume Integral Equations

Fan

Chen²,

Chen³

et al. 2009

PIER

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Abstract-Electromagnetic scattering problems involving inhomogeneous objects can be numerically solved by applying a method of moment's discretization to the hypersingular volume integral equation in which a grad-div operator acts on a vector potential. The vector potential is a spatial convolution of the free space Green's function and the contrast source over the domain of interest. For electrically large problems, the direct solution of the resulting linear system is expensive, both computationally and in memory use. Conventionally, the fast Fourier transform method (FFT) combined Krylov subspace iterative approaches are adopted. However, the uniform discretization required by FFT is not ideal for those problems involving inhomogeneous scatterers and sharp discontinuities. In this paper, a nonuniform FFT method combined weak form integral equation technique is presented. The method performs better in terms of speed and memory use than FFT on the configuration involving both the electrically large and fine structures. This is illustrated by a representative numerical test case.

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Section: Weak Form Testing and Expansion Proceduresmentioning

confidence: 99%

Section: Weak Form Testing and Expansion Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Weak Form Nonuniform Fast Fourier Transform Method for Solving Volume Integral Equations

Fan

Chen²,

Chen³

et al. 2009

PIER

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show abstract

“…The k-space method uses the Krylov-subspace iterative method to solve the integral equation, and the required matrix-vector product in the iteration is efficiently evaluated by using the fast Fourier transform (FFT) technique. A large number of related papers have been reported by many researchers, which can be found in [3][4][5][6][7][8]. Among these schemes, the conjugate gradient (CG)-FFT method developed by Zwamborn and van den Berg in the 1990s leads to a weaker singularity in the dyadic Green's function and appears to be simpler to implement [3].…”

Section: Introductionmentioning

confidence: 99%

“…Among these schemes, the conjugate gradient (CG)-FFT method developed by Zwamborn and van den Berg in the 1990s leads to a weaker singularity in the dyadic Green's function and appears to be simpler to implement [3]. Recently, Liu's group developed a fast weak-form biconjugate gradient (BCG)-FFT method [4], which shows promising results because of a faster convergence speed than the conventional weak-form CG-FFT method. They further improved the convergence speed by using the weak-form discretization with the stabilized BCG (BCGS) method, which is referred to as BCGS-FFT method [5].…”

Section: Introductionmentioning

confidence: 99%

Adaptively Accelerated Gmres Fast Fourier Transform Method for Electromagnetic Scattering

Xin¹,

Rui²

2008

PIER

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Abstract-The problem of electromagnetic scattering by 3D dielectric bodies is formulated in terms of a weak-form volume integral equation. Applying Galerkin's method with rooftop functions as basis and testing functions, the integral equation can be usually solved by Krylov-subspace fast Fourier transform (FFT) iterative methods. In this paper, the generalized minimum residual (GMRES)-FFT method is used to solve this integral equation, and several adaptive acceleration techniques are proposed to improve the convergence rate of the GMRES-FFT method. On several electromagnetic scattering problems, the performance of these adaptively accelerated GMRES-FFT methods are thoroughly analyzed and compared.

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Iterative implementation of approximate solutions for electromagnetic scattering

Nakhkash

2007

Micro & Optical Tech Letters

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A 2.4-GHz WLAN receiver fabricated by 90-nm RF CMOS technology, using SIP with external matching networks for the dual IF double downconversion applications has been demonstrated. A high power gain of 36.24 dB with a low DSB noise figure of 2.68 dB has been achieved in an available linearity operation. Therefore, this proposed circuit could improve the design flexibility of back-end stages. , A high gain and low supply voltage LNA for the direct conversion application with 4-KV HBM ESD protection in 90-nm RF CMOS, IEEE Microwave Wireless Compon Lett 16 (2006), 612-614. 3. K.R. Rao, J. Wilson, and M. Ismail, A CMOS RF front-end for a multistandard WLAN receiver, IEEE Microwave Wireless Compon Lett 15 (2005), 321-323. 4. K.High-performance large-inductance embedded inductors in thin array plastic packaging (TAPP) for RF system-in-package applications, ABSTRACT: This article introduces a recursive formula, in which any approximate method can, iteratively, be incorporated to solve electromagnetic scattering problems. The use of extended Born approximation and quasi-analytical approximation in this formula results in two series (algorithms), whose convergence properties are discussed. Numerical examples are given to demonstrate merits and the range of applicability of the new series.This example aims at the study of the IEBA, IQA, and HOGEBA algorithms at low frequencies for two models as follows:Model 1: R ϭ 100 cm, ⌬␦ ϭ 20 mm, b ϭ 0 , b ϭ 0 ϭ 5 0 , ϭ 100 mS/m, source ϭ PW

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Three‐dimensional weak‐form conjugate‐ and biconjugate‐gradient FFT methods for volume integral equations

Cited by 19 publications

References 0 publications

Weak Form Nonuniform Fast Fourier Transform Method for Solving Volume Integral Equations

Weak Form Nonuniform Fast Fourier Transform Method for Solving Volume Integral Equations

Adaptively Accelerated Gmres Fast Fourier Transform Method for Electromagnetic Scattering

Iterative implementation of approximate solutions for electromagnetic scattering

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