Global energy-tracking identities and global energy-tracking splitting FDTD schemes for the Drude Models of Maxwell's equations in three-dimensional metamaterials

Wanshan Li, Dong Liang, Yanping Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)

Abstract

In this article, we study the Drude models of Maxwell's equations in three-dimensional metamaterials. We derive new global energy-tracking identities for the three dimensional electromagnetic problems in the Drude metamaterials, which describe the invariance of global electromagnetic energy in variation forms. We propose the time second-order global energy-tracking splitting FDTD schemes for the Drude model in three dimensions. The significant feature is that the developed schemes are global energy-preserving, unconditionally stable, second-order accurate both in time and space, and computationally efficient. We rigorously prove that the new schemes satisfy these energy-tracking identities in the discrete form and the discrete variation form and are unconditionally stable. We prove that the schemes in metamaterials are second order both in time and space. The superconvergence of the schemes in the discrete H1norm is further obtained to be second order both in time and space. Their approximations of divergence-free are also analyzed to have second-order accuracy both in time and space. Numerical experiments confirm our theoretical analysis results. Numer Methods Partial Differential Eq 33: 763–785, 2017.
Original languageEnglish
Pages (from-to)763-785
Number of pages23
JournalNumerical Methods for Partial Differential Equations
Volume33
Issue number3
DOIs
Publication statusPublished - 1 May 2017

Keywords

  • Drude models of Maxwell's equations in metamaterials
  • GET-S-FDTD
  • global energy-tracking identities
  • optimal error estimates
  • second order in time and space
  • superconvergence
  • three dimensions
  • unconditional stability

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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