On the Solution of Time-Harmonic Scattering Problems for Maxwell’s Equations

Hazard, Christophe; Lenoir, M.

doi:10.1137/s0036141094271259

Cited by 137 publications

(168 citation statements)

References 15 publications

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“…We seek solutions E, H ∈ H loc (curl; R 3 ) to (1.8); see [19,22,23,31] for the well-posedness of the scattering system (1.8). Here and also in what follows, we shall often use the spaces H loc (curl; X) = {U | B ∈ H(curl; B); B is any bounded subdomain of X} and…”

Section: Mathematical Formulationmentioning

confidence: 99%

Full and Partial Cloaking in Electromagnetic Scattering

Deng

Liu

Uhlmann

2016

Arch Rational Mech Anal

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Abstract. In this paper, we consider two regularized transformation-optics cloaking schemes for electromagnetic (EM) waves. Both schemes are based on the blowup construction with the generating sets being, respectively, a generic curve and a planar subset. We derive sharp asymptotic estimates in assessing the cloaking performances of the two constructions in terms of the regularization parameters and the geometries of the cloaking devices. The first construction yields an approximate full-cloak, whereas the second construction yields an approximate partial-cloak. Moreover, by incorporating properly chosen conducting layers, both cloaking constructions are capable of nearly cloaking arbitrary EM contents. This work complements the existing results in [5][6][7] on approximate EM cloaks with the generating set being a singular point, and it also extends [9, 25] on regularized full and partial cloaks for acoustic waves governed by the Helmholtz system to the more challenging EM case governed by the full Maxwell system.

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Section: Mathematical Formulationmentioning

confidence: 99%

Full and Partial Cloaking in Electromagnetic Scattering

Deng

Liu

Uhlmann

2016

Arch Rational Mech Anal

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“…Consequently the nonzero eigenvalues of interest can be captured by choosing the parameter s large enough (or by taking different values of s). In that respect, our method is similar to the discrete regularization method for standard edge elements [3,18] and can be compared with the so-called grad-div regularizated method for the continuous Maxwell's problem where the term s Ω div u div v is added to the standard bilinear form of the curl [13,16].…”

Section: Some Numerical Testsmentioning

confidence: 99%

Discrete compactness for a discontinuous Galerkin approximation of Maxwell's system

Creusé¹,

Nicaise²

2006

ESAIM: M2AN

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Abstract. In this paper we prove the discrete compactness property for a discontinuous Galerkin approximation of Maxwell's system on quite general tetrahedral meshes. As a consequence, a discrete Friedrichs inequality is obtained and the convergence of the discrete eigenvalues to the continuous ones is deduced using the theory of collectively compact operators. Some numerical experiments confirm the theoretical predictions.Mathematics Subject Classification. 65N25, 65N30.

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“…The scattered fields have to satisfy the Silver-Müller radiation conditions (5). As a consequence of Rellich's lemma and the unique continuation principle, the transmission problem (2)-(5) has a unique solution [10,20].…”

Section: Mathematical Modelmentioning

confidence: 99%

Direct boundary integral equation method for electromagnetic scattering by partly coated dielectric objects

Cranganu-Cretu

Hiptmair

2005

Comput. Visual Sci.

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We present a new variational direct boundary integral equation approach for solving the scattering and transmission problem for dielectric objects partially coated with a PEC layer. The main idea is to use the electromagnetic Calderón projector along with transmission conditions for the electromagnetic fields. This leads to a symmetric variational formulation which lends itself to Galerkin discretization by means of divergence-conforming discrete surface currents. A wide array of numerical experiments confirms the efficacy of the new method.Keywords Electromagnetic scattering · Direct boundary integral equations · Galerkin boundary element method (BEM)

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On the Solution of Time-Harmonic Scattering Problems for Maxwell’s Equations

Cited by 137 publications

References 15 publications

Full and Partial Cloaking in Electromagnetic Scattering

Full and Partial Cloaking in Electromagnetic Scattering

Discrete compactness for a discontinuous Galerkin approximation of Maxwell's system

Direct boundary integral equation method for electromagnetic scattering by partly coated dielectric objects

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