Transformation optics based local mesh refinement for solving Maxwell's equations

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

In this paper, a novel local mesh refinement algorithm based on transformation optics (TO) has been developed for solving the Maxwell's equations of electrodynamics. The new algorithm applies transformation optics to enlarge a small region so that it can be resolved by larger grid cells. The transformed anisotropic Maxwell's equations can be stably solved by an anisotropic FDTD method, while other subgridding or adaptive mesh refinement FDTD methods require time-space field interpolations and often suffer from the late-time instability problem. To avoid small time steps introduced by the transformation optics approach, an additional application of the mapping of the material matrix to a dispersive material model is employed. Numerical examples on scattering problems of dielectric and dispersive objects illustrate the performance and the efficiency of the transformation optics based FDTD method.

Original languageEnglish (US)
Pages (from-to)359-370
Number of pages12
JournalJournal of Computational Physics
Volume258
DOIs
StatePublished - Feb 1 2014

Fingerprint

Maxwell equations
Maxwell equation
Optics
finite difference time domain method
optics
matrix materials
Electrodynamics
electrodynamics
interpolation
Interpolation
grids
Scattering
cells
scattering

Keywords

  • FDTD
  • Local mesh refinement
  • Maxwell's equations
  • Subgridding
  • Transformation optics

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy (miscellaneous)

Cite this

Transformation optics based local mesh refinement for solving Maxwell's equations. / Liu, Jinjie; Brio, Moysey; Moloney, Jerome V.

In: Journal of Computational Physics, Vol. 258, 01.02.2014, p. 359-370.

Research output: Contribution to journalArticle

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