Analysis of electromagnetic scattering from an overfilled cavity in the ground plane

Wood, Aihua W.

doi:10.1016/j.jcp.2005.11.007

Cited by 52 publications

(45 citation statements)

References 23 publications

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“…A variety of numerical methods, including the method of moments, finite difference, finite element, boundary element method, and hybrid methods [3,7,9,10], have been developed to characterize the scattering from cavities. Some mathematical analysis and numerical treatments on the open cavities can be found in [1,2,5].…”

Section: Introductionmentioning

confidence: 99%

A Fast High Order Method for Electromagnetic Scattering by Large Open Cavities

Zhao

Qiao

Tang

2011

JCM

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In this paper, the electromagnetic scattering from a rectangular large open cavity embedded in an infinite ground plane is studied. By introducing a nonlocal artificial boundary condition, the scattering problem from the open cavity is reduced to a bounded domain problem. A compact fourth order finite difference scheme is then proposed to discrete the cavity scattering model in the rectangular domain, and a special treatment is enforced to approximate the boundary condition, which makes truncation errors reach O(h 4 ) in the whole computational domain. A fast algorithm, exploiting the discrete Fourier transformation in the horizontal and a Gaussian elimination in the vertical direction, is employed, which reduces the discrete system to a much smaller interface system. An effective preconditioner is presented for the BICGstab iterative solver to solve this interface system. Numerical results demonstrate the remarkable accuracy and efficiency of the proposed method. In particular, it can be used to solve the cavity model for the large wave number up to 600π.Mathematics subject classification: 65N06, 78M20.

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Section: Introductionmentioning

confidence: 99%

A Fast High Order Method for Electromagnetic Scattering by Large Open Cavities

Zhao

Qiao

Tang

2011

JCM

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“…The problem (2.1) can be solved by a standard variational method [26,43]. For the rectangular cavity with a homogeneous medium, we can get another transparent boundary condition on the aperture of the cavity, which produces a smaller computational domain.…”

Section: Tm Polarizationmentioning

confidence: 99%

“…The theoretical analysis of scattering from cavities was well investigated (see, for example, [3,4,43]). A variety of numerical methods, including finite difference method [7,[13][14][15][16][17]41,42], finite element method [2,28,31,32,38,40,[48][49][50], boundary element method [21,44,47] and hybrid method [25,30,36,47] have been developed for solving the cavity problem.…”

Section: Introductionmentioning

confidence: 99%

“…An important step of these methods is to introduce a TBC to reduce the unbounded domain problem to a bounded one. For example, by introducing a TBC on a semicircle, Wood [43] presented a finite element/Fourier series method for analyzing the overfilled cavity problem. In this paper, for overfilled cavities with slender structures or overfilled multiple cavities [2,8,11,12,18,34,35,37] (see Fig.…”

Section: Introductionmentioning

confidence: 99%

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Two transparent boundary conditions for the electromagnetic scattering from two-dimensional overfilled cavities

Du¹

2011

Journal of Computational Physics

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“…The challenging mathematical issue is to establish the stability estimates with explicit dependence on the high wavenumber [12,13,27], which help us gain a deeper understanding on high frequency problems. To include the analysis for more complex geometries, the overfilled cavity problems were investigated in [16,31,42], where the inhomogeneous medium filling the cavity interior was allowed to protrude into the space above the ground surface; the multiple cavity scattering problem was studied in [30], where the cavity was consisted of finitely many disjoint components.…”

Section: Introductionmentioning

confidence: 99%

A Survey of Open Cavity Scattering Problems

Li¹

2018

JCM

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This paper gives a brief survey of recent developments on mathematical modeling and analysis of the open cavity scattering problems, which arise in diverse scientific areas and have significant industrial and military applications. The scattering problems are studied for the two-dimensional Helmholtz equation corresponding to the transverse magnetic or electric polarization, and the three-dimensional time-harmonic and time-domain Maxwell equations. Since these problems are imposed in open domains, a key step of the analysis is to develop transparent boundary conditions and reformulate them equivalently into boundary value problems in bounded domains. The well-posedness of weak solutions are shown for the associated variational problems by using either the Lax-Milgram theorem or the Fredholm alternative. Mathematics subject classification: 35Q61, 78A25, 78M30

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Analysis of electromagnetic scattering from an overfilled cavity in the ground plane

Cited by 52 publications

References 23 publications

A Fast High Order Method for Electromagnetic Scattering by Large Open Cavities

A Fast High Order Method for Electromagnetic Scattering by Large Open Cavities

Two transparent boundary conditions for the electromagnetic scattering from two-dimensional overfilled cavities

A Survey of Open Cavity Scattering Problems

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