A Staggered Fourth-Order Accurate Explicit Finite Difference Scheme for the Time-Domain Maxwell's Equations

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Abstract

We consider a model explicit fourth-order staggered finite-difference method for the hyperbolic Maxwell's equations. Appropriate fourth-order accurate extrapolation and one-sided difference operators are derived in order to complete the scheme near metal boundaries and dielectric interfaces. An eigenvalue analysis of the overall scheme provides a necessary, but not sufficient, stability condition and indicates long-time stability. Numerical results verify both the stability analysis, and the scheme's fourth-order convergence rate over complex domains that include dielectric interfaces and perfectly conducting surfaces. For a fixed error level, we find the fourth-order scheme is computationally cheaper in comparison to the Yee scheme by more than an order of magnitude. Some open problems encountered in the application of such high-order schemes are also discussed.

Original languageEnglish (US)
Pages (from-to)286-315
Number of pages30
JournalJournal of Computational Physics
Volume168
Issue number2
DOIs
StatePublished - Apr 10 2001

All Science Journal Classification (ASJC) codes

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

Keywords

  • Maxwell's equations, staggered finite-difference schemes, fourth-order schemes, FD-TD scheme

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