Method of moving frames to solve time-dependent Maxwell's equations on anisotropic curved surfaces: Applications to invisible cloak and ELF propagation

Applying the method of moving frames to Maxwell's equations yields two important advancements for scientific computing. The first is the use of upwind flux for anisotropic materials in Maxwell's equations, especially in the context of discontinuous Galerkin (DG) methods. Upwind flux has be...

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Bibliographic Details
Published in:Journal of computational physics 2017-07, Vol.340, p.85-104
Main Author: Chun, Sehun
Format: Article
Language:English
Subjects:
Anisotropic curved surface
Anisotropic media
Anisotropy
Computational physics
Computer simulation
Discontinuous Galerkin method
Extremely low frequencies
Extremely low frequency (ELF) propagation
Finite element method
Frames
Frequencies
Galerkin method
Invisible cloak
Isotropic material
Mathematical functions
Mathematical models
Maxwell's equations
Metamaterials
Partial differential equations
Propagation
Stealth technology
Time dependence
Upwind flux
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Summary:Applying the method of moving frames to Maxwell's equations yields two important advancements for scientific computing. The first is the use of upwind flux for anisotropic materials in Maxwell's equations, especially in the context of discontinuous Galerkin (DG) methods. Upwind flux has been available only to isotropic material, because of the difficulty of satisfying the Rankine–Hugoniot conditions in anisotropic media. The second is to solve numerically Maxwell's equations on curved surfaces without the metric tensor and composite meshes. For numerical validation, spectral convergences are displayed for both two-dimensional anisotropic media and isotropic spheres. In the first application, invisible two-dimensional metamaterial cloaks are simulated with a relatively coarse mesh by both the lossless Drude model and the piecewisely-parametered layered model. In the second application, extremely low frequency propagation on various surfaces such as spheres, irregular surfaces, and non-convex surfaces is demonstrated.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2017.03.031