Analysis of finite structures using the CG-FFT method and discretizing Green's function in the spectral domain

Gago, E.; Cátedra, M.F.

doi:10.1109/aps.1989.134676

Cited by 2 publications

(2 citation statements)

References 6 publications

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“…For the open PEC cylindrical surface, the exact equivalent magnetic and electric surface currents (M ± s , J ± s ) can be found through the Electric Field Integral Equation (EFIE) or Magnetic Field Integral Equation (MFIE) [26,27], with the help of (26) and (29). For EFIE, only the front-wave on the cylindrical surface, i.e.,Ẽ >+ < (ρ 0 ), is considered, which should satisfy the boundary condition on the inner/outer (-/+) cylindrical surface, i.e.,n ± ×Ẽ (17), (26) and (29), it is not difficult to obtain the exact equivalent magnetic and electric surface currents (M ± s , J ± s ) as follows,…”

Section: The Correction To the Image Approximationmentioning

confidence: 99%

On the Image Approximation for Electromagnetic Wave Propagation and Pec Scattering in Cylindrical Harmonics

Liao¹,

Vernon²

2006

PIER

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Abstract-A closed-form formula, the discrepancy parameter, which has been defined as the ratio of the modal expansion coefficients between the electromagnetic field obtained from the image approximation and the incident electromagnetic field, has been proposed for the evaluation of the validity of the image approximation in the electromagnetic wave propagation, i.e., Love's equivalence principle, and the electromagnetic wave scattering, i.e., the induction equivalent and the physical equivalent, in the cylindrical geometry. The discrepancy parameter is derived through two equivalent methods, i.e., the vector potential method through the cylindrical addition theorem and the dyadic Green's function method, for both the TE and TM cylindrical harmonics. The discrepancy parameter justifies the fact that the image approximation approaches the exact solution for the cylindrical surface of infinite radius. For the narrow-band field with limited spectral component in k space, the cylindrical modal expansion of the electromagnetic wave into the TE and TM cylindrical harmonics can be separated into the forward-propagating wave that propagates forward and the back-scattered wave that is back-scattered by the PEC surface, within the image approximation. The discrepancy parameter shows that the validity of the image approximation depends on the property of the incident field and the radius of the cylindrical surface, i.e., the narrow-band field and the surface of a large radius are in favor of the image approximation, which has also been confirmed by the numerical result. Liao and Vernon

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Section: The Correction To the Image Approximationmentioning

confidence: 99%

On the Image Approximation for Electromagnetic Wave Propagation and Pec Scattering in Cylindrical Harmonics

Liao¹,

Vernon²

2006

PIER

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“…The MoM requires O(N 2 ) computer memory and O(N 3 ) computation time because of the need to store and invert the MoM matrix [3], where N is the number of unknowns in the problem. An important improvement over the MoM is conjugate gradient -fast Fourier transform method (CG-FFT) [4][5][6][7][8][9][10][11][12][13][14]. It uses conjugate gradient algorithm (CG), one of the Krylov subspace iterative approaches [15], to solve the integral equation, and the required matrix-vector product during the iteration is efficiently evaluated by using the fast Fourier transform (FFT) scheme.…”

Section: Introductionmentioning

confidence: 99%

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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Analysis of finite structures using the CG-FFT method and discretizing Green's function in the spectral domain

Cited by 2 publications

References 6 publications

On the Image Approximation for Electromagnetic Wave Propagation and Pec Scattering in Cylindrical Harmonics

On the Image Approximation for Electromagnetic Wave Propagation and Pec Scattering in Cylindrical Harmonics

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

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