Zur Theorie elektromagnetischer Schwingungen in anisotropen inhomogenen Medien

Leis, Rolf

doi:10.1007/bf01110135

Cited by 77 publications

(52 citation statements)

References 9 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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“…Using the identity for P and weakly enforcing the boundary condition P (∇·E)| ∂Ω = 0 is an easy fix (at least for the boundary value problem (1.1) with ω = 0), but it is also a bad idea when X h is composed of C 0 -Lagrange finite elements, since it implies that any solution to (3.2) satisfies a uniform bound in H 0 (curl, Ω) ∩ H(div, Ω); see e.g. [28,34]. It is known since the ground-breaking work of Costabel [18] that any H 1 -conforming method that is uniformly stable in H 0 (curl, Ω) ∩ H(div, Ω) cannot converge if Ω is nonsmooth and non-convex.…”

Section: The H −α Penaltymentioning

confidence: 99%

Approximation of the eigenvalue problem for the time harmonic Maxwell system by continuous Lagrange finite elements

Bonito

Guermond

2011

Math. Comp.

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“…The idea goes back to LEIS [53] and consists in blowing up the kernel K by transforming the eigenvalue zero into a family of non-zero spurious eigenvalues. This is easily done, at the continuous level, by the introduction of a parameter s > 0 and a new bilinear form -note that a 0 coincides with the curl form (5.1),…”

Section: A the Principlementioning

confidence: 99%

Computation of resonance frequencies for Maxwell equations in non-smooth domains

Costabel

Dauge

2003

Lecture Notes in Computational Science and Engineering

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Summary. We address the computation by finite elements of the non-zero eigenvalues of the (curl, curl) bilinear form with perfect conductor boundary conditions in a polyhedral cavity. One encounters two main difficulties: (i) The infinite dimensional kernel of this bilinear form (the gradient fields), (ii) The unbounded singularities of the eigen-fields near corners and edges of the cavity. We first list possible variational spaces with their functional properties and provide a short description of the edge and corner singularities. Then we address different formulations using a Galerkin approximation by edge elements or nodal elements.After a presentation of edge elements, we concentrate on the functional issues connected with the use of nodal elements. In the framework of conforming methods, nodal elements are mandatory if one regularizes the bilinear form (curl, curl) in order to get rid of the gradient fields. A plain regularization with the (div, div) bilinear form converges to a wrong solution if the domain has reentrant edges or corners. But remedies do exist. We will present the method of addition of singular functions, and the method of regularization with weight, where the (div, div) bilinear form is modified by the introduction of a weight which can be taken as the distance to reentrant edges or corners.

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Zur Theorie elektromagnetischer Schwingungen in anisotropen inhomogenen Medien

Cited by 77 publications

References 9 publications

Full and Partial Cloaking in Electromagnetic Scattering

Full and Partial Cloaking in Electromagnetic Scattering

Approximation of the eigenvalue problem for the time harmonic Maxwell system by continuous Lagrange finite elements

Computation of resonance frequencies for Maxwell equations in non-smooth domains

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