An integral equation method for the electromagnetic scattering from cavities

Ammari, Habib; Bao, Gang; Wood, Aihua W.

doi:10.1002/1099-1476(200008)23:12<1057::aid-mma151>3.0.co;2-6

Cited by 103 publications

(88 citation statements)

References 12 publications

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“…In the context of design, an optimization procedure was used to enhance or reduce the RCS in [7,8]. A great deal of mathematical and computational methods have been studied for the scattering by cavities, including variational and finite element methods ( [2,4]), integral equation methods ( [1,3,5,25]), time-domain methods ( [21][22][23][24]), and hybrid methods ( [6,10,15,16,19,20]). The goal of this work is to establish the stability estimates of cavity problems with explicit dependence on the high wavenumber.…”

Section: Introductionmentioning

confidence: 85%

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Stability for the Electromagnetic Scattering from Large Cavities

Bao

Yun

2015

Arch Rational Mech Anal

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Consider the scattering of electromagnetic waves from a large rectangular cavity embedded in the infinite ground plane. There are two fundamental polarizations for the scattering problem in two dimensions: TM (transverse magnetic) and TE (transverse electric). In this paper, new stability results for the cavity problems are established for large rectangular shape cavities in both polarizations. For the TM cavity problem, an asymptotic property of the solution and a stability estimate with an improved dependence on the high wavenumber are derived. In the TE case, the first stability result is established with an explicit dependence on the wave number.

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Section: Introductionmentioning

confidence: 85%

“…Hereũ n is defined asũ n (x, y) = u n (y) sin(nx) for n ∈ Z, as given in (3). Note that sin k 2 − n 2 y = i sinh n 2 − k 2 y for any |n| > k.…”

Section: Tm Cavity: the Proof Of Theorem 21mentioning

confidence: 99%

Stability for the Electromagnetic Scattering from Large Cavities

Bao

Yun

2015

Arch Rational Mech Anal

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“…Mathematical analysis of the problems were done in three fundamental papers [2][3][4], where transparent boundary conditions, based on the Fourier transform, were proposed on the opening. As the applied mathematics community has begun to work on these problems, there has been a rapid development of the theory, analysis, and computational techniques in this area.…”

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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“…Recently, in [1,2], Ammari and Bao developed a variational approach for solving the cavity problems in two-and three-dimensional media, and studied the well-posedness of the problem. They also investigated the problem by an integral equation method in [3]. In [18], we introduced a perfectly matched layer in curvilinear coordinates to study the locally perturbed half plane problems (including the cavity problems), and presented several numerical results.…”

Section: Introductionmentioning

confidence: 99%

A Finite Element Method with Rectangular Perfectly Matched Layers for the Scattering from Cavities

Zhang¹

2009

JCM

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We develop a finite element method with rectangular perfectly matched layers (PMLs) for the wave scattering from two-dimensional cavities. The unbounded computational domain is truncated to a bounded one by using of a rectangular perfectly matched layer at the open aperture. The PML parameters such as the thickness of the layer and the fictitious medium property are determined through sharp a posteriori error estimates. Numerical experiments are carried out to illustrate the competitive behavior of the proposed method.Mathematics subject classification: 35Q60, 65L60, 78A45.

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An integral equation method for the electromagnetic scattering from cavities

Cited by 103 publications

References 12 publications

Stability for the Electromagnetic Scattering from Large Cavities

Stability for the Electromagnetic Scattering from Large Cavities

A Survey of Open Cavity Scattering Problems

A Finite Element Method with Rectangular Perfectly Matched Layers for the Scattering from Cavities

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