FDTD BASED SECOND-ORDER ACCURATE LOCAL MESH REFINEMENT METHOD FOR MAXWELL'S EQUATIONS IN TWO SPACE DIMENSIONS ¤

A. R. Zakharian, M. Brio, Jerome V Moloney

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

An algorithm is presented for local space-time mesh re¯nement appropriate for electromagnetic simulations based on the space-time staggered FDTD method. The method is based on the adaptive mesh renement algorithm originally developed for hyperbolic conservation laws. Analysis of the dispersion relation and of the numerical reflection and transmission coefficients in one and two space dimensions shows that a scheme based on linear interpolation at the grid interfaces is unstable due to reflection coe±cient >1 at frequencies above the cutoff frequency of the coarse grid. A second-order accurate algorithm based on higher-order interpolations that enforces conservation of the magnetic field circulation at the fine-coarse grid boundaries is constructed. The new algorithm is shown to be stable and accurate for long time integration. A numerical simulation of an optical ring microcavity resonator using multilevel grid refinement in two space dimensions is presented.

Original languageEnglish (US)
Pages (from-to)497-513
Number of pages17
JournalCommunications in Mathematical Sciences
Volume2
Issue number3
DOIs
StatePublished - 2004

Keywords

  • Amr
  • Computational electrodynamics
  • Fdtd
  • Grid interfaces
  • Maxwell's equations
  • Mesh refinement
  • Numerical simulation
  • Optical waveguide
  • Subgridding

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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