Method of moving frames to solve time-dependent Maxwell's equations on anisotropic curved surfaces

Applications to invisible cloak and ELF propagation

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)85-104
Number of pages20
JournalJournal of Computational Physics
Volume340
DOIs
Publication statusPublished - 2017 Jul 1

Fingerprint

curved surfaces
Maxwell equations
Maxwell equation
anisotropic media
Anisotropic media
propagation
mesh
extremely low frequencies
Galerkin method
Fluxes
Natural sciences computing
Metamaterials
Galerkin methods
tensors
Tensors
composite materials
Composite materials

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Cite this

@article{5d87b6f015c849658b4c5b6affb03705,
title = "Method of moving frames to solve time-dependent Maxwell's equations on anisotropic curved surfaces: Applications to invisible cloak and ELF propagation",
abstract = "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.",
author = "Sehun Chun",
year = "2017",
month = "7",
day = "1",
doi = "10.1016/j.jcp.2017.03.031",
language = "English",
volume = "340",
pages = "85--104",
journal = "Journal of Computational Physics",
issn = "0021-9991",
publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Method of moving frames to solve time-dependent Maxwell's equations on anisotropic curved surfaces

T2 - Applications to invisible cloak and ELF propagation

AU - Chun, Sehun

PY - 2017/7/1

Y1 - 2017/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85016425609&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85016425609&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2017.03.031

DO - 10.1016/j.jcp.2017.03.031

M3 - Article

VL - 340

SP - 85

EP - 104

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -