Hodge decomposition for two‐dimensional time‐harmonic Maxwell's equations: impedance boundary condition

Abstract

We extend the Hodge decomposition approach for the cavity problem of two‐dimensional time‐harmonic Maxwell's equations to include the impedance boundary condition, with anisotropic electric permittivity and sign‐changing magnetic permeability. We derive error estimates for a P1 finite element method based on the Hodge decomposition approach and present results of numerical experiments that involve metamaterials and electromagnetic cloaking. The well‐posedness of the cavity problem when both electric permittivity and magnetic permeability can change sign is also discussed. Copyright © 2015 John Wiley & Sons, Ltd.

On the use of Perfectly Matched Layers at corners for scattering problems with sign-changing coefficients

“…Let B denote the operator associated with the sesquilinear form b(•, •) defined by (15) where I : H 1 (D R ) → H 1 (D R ) is an isomorphism and where K :…”

“…Under some assumptions on the meshes, the discretized problem is well-posed and its solution converges to the solution of the continuous problem. Let us mention that the study of Maxwell's equations has been carried out in [10,11,15].…”

Developing Finite Element Methods for Simulating Transformation Optics Devices with Metamaterials

“…where ǫ 0 and µ 0 are the permittivity and permeability of vacuum, and ǫ and µ are the relative permittivity and permeability of the specific media. There exist many excellent works on the analysis and applications of finite element method (FEM) for solving the Maxwell's equations in various media, such as in the free space (e.g., papers [3,4,6,7,11,16,17,43], books [12,22,30] and references therein); in general dispersive media (e.g., [2,19,28,34]); in negative index metamaterials [18,38,39]; and in cloaking metamaterials [23][24][25]41]. In recent years, we developed some mathematical models and time-domain FEMs for simulating the invisibility cloaks [23][24][25].…”

Nonlocal models for interface problems between dielectrics and metamaterials

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