High-order accurate modeling of electromagnetic wave propagation across media - Grid conforming bodies

Eugene Kashdan, Eli Turkel*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The Maxwell equations contain a dielectric permittivity ε that describes the particular media. For homogeneous materials at low temperatures this coefficient is constant within a material. However, it jumps at the interface between different media. This discontinuity can significantly reduce the order of accuracy of the numerical scheme. We solve the Maxwell equations, with an interface between two media, using a fourth-order accurate algorithm. We regularize the discontinuous dielectric permittivity by a continuous function either locally, near the interface, or globally, in the entire domain. We study the effect of this regularization on the order of accuracy for a one-dimensional time-dependent problem. We then implement this for the three-dimensional Maxwell equations in spherical coordinates with appropriate physical and artificial absorbing boundary conditions. We use Fourier filtering of the high frequency modes near the poles to increase the time-step.

Original languageEnglish
Pages (from-to)816-835
Number of pages20
JournalJournal of Computational Physics
Volume218
Issue number2
DOIs
StatePublished - 1 Nov 2006

Keywords

  • CEM
  • Discontinuities
  • Discontinuous coefficients
  • FDTD
  • High-order accuracy
  • High-order methods
  • Time-dependent Maxwell equations

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