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T-coercivity for scalar interface problems between dielectrics and metamaterials
Published online by Cambridge University Press: 11 April 2012
Abstract
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Some electromagnetic materials have, in a given frequency range, an effective dielectric permittivity and/or a magnetic permeability which are real-valued negative coefficients when dissipation is neglected. They are usually called metamaterials. We study a scalar transmission problem between a classical dielectric material and a metamaterial, set in an open, bounded subset of Rd, with d = 2,3. Our aim is to characterize occurences where the problem is well-posed within the Fredholm (or coercive + compact) framework. For that, we build some criteria, based on the geometry of the interface between the dielectric and the metamaterial. The proofs combine simple geometrical arguments with the approach of T-coercivity, introduced by the first and third authors and co-worker. Furthermore, the use of localization techniques allows us to derive well-posedness under conditions that involve the knowledge of the coefficients only near the interface. When the coefficients are piecewise constant, we establish the optimality of the criteria.
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- Research Article
- Information
- ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 6 , November 2012 , pp. 1363 - 1387
- Copyright
- © EDP Sciences, SMAI, 2012
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