Two-dimensional Maxwell's equations with sign-changing coefficients

Anne-Sophie Bonnet-Ben Dhia 1 Lucas Chesnel 1 Patrick Ciarlet 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : We consider the theoretical study of time harmonic Maxwellʼs equations in presence of sign-changing coefficients, in a two-dimensional configuration. Classically, the problems for both the Transverse Magnetic and the Transverse Electric polarizations reduce to an equivalent scalar Helmholtz type equation. For this scalar equation, we have already studied consequences of the presence of sign-changing coefficients in previous papers, and we summarize here the main results. Then we focus on the alternative approach which relies on the two-dimensional vectorial formulations of the TM or TE problems, and we exhibit some unexpected effects of the sign-change of the coefficients. In the process, we provide new results on the scalar equations.
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https://hal.inria.fr/hal-00937769
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Submitted on : Tuesday, January 28, 2014 - 6:06:08 PM
Last modification on : Wednesday, July 3, 2019 - 10:48:03 AM

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Anne-Sophie Bonnet-Ben Dhia, Lucas Chesnel, Patrick Ciarlet. Two-dimensional Maxwell's equations with sign-changing coefficients. Applied Numerical Mathematics, Elsevier, 2013, ⟨10.1016/j.apnum.2013.04.006⟩. ⟨hal-00937769⟩

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