On Time-Domain NRBC for Maxwell’s Equations and Its Application in Accurate Simulation of Electromagnetic Invisibility Cloaks

Bo Wang, Zhiguo Yang, Li Lian Wang, Shidong Jiang

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we present analytic formulas of the temporal convolution kernel functions involved in the time-domain non-reflecting boundary condition (NRBC) for the electromagnetic scattering problems. Such exact formulas themselves lead to accurate and efficient algorithms for computing the NRBC for domain reduction of the time-domain Maxwell’s system in R3. A second purpose of this paper is to derive a new time-domain model for the electromagnetic invisibility cloak. Different from the existing models, it contains only one unknown field and the seemingly complicated convolutions can be computed as efficiently as the temporal convolutions in the NRBC. The governing equation in the cloaking layer is valid for general geometry, e.g., a spherical or polygonal layer. Here, we aim at simulating the spherical invisibility cloak. We take the advantage of radially stratified dispersive media and special geometry, and develop an efficient vector spherical harmonic-spectral-element method for its accurate simulation. Compared with limited results on FDTD simulation, the proposed method is optimal in both accuracy and computational cost. Indeed, the saving in computational time is significant.

Original languageEnglish (US)
Article number20
JournalJournal of Scientific Computing
Volume86
Issue number2
DOIs
StatePublished - Feb 2021

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Anisotropic and dispersive medium
  • Convolution
  • Electromagnetic wave scattering
  • Invisibility cloaking
  • Maxwell’s system
  • Non-reflecting boundary condition

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