Application of Symmetric Hyperbolic Systems for the Time-Dependent Maxwell's Equations in Bi-Anisotropic Media

Yakhno V. G., Yakhno T. M.

CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, vol.80, pp.233-250, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 80
  • Publication Date: 2011
  • Journal Name: CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.233-250
  • Keywords: Maxwell's equations, bi-anisotropic material, symmetric hyperbolic system, analytical method, simulation
  • Dokuz Eylül University Affiliated: Yes

Abstract

The time-dependent Maxwell's equations in non-dispersive homogeneous bi-anisotropic materials are considered in the paper. These equations are written as a symmetric hyperbolic system. A new method of the computation of the electric and magnetic fields arising from electric current is suggested in the paper. This method consists of the following. The Maxwell's equations are written in terms of the Fourier transform with respect to the space variables. The Fourier image of the obtained system is a system of ordinary differential equations whose coefficients depend on the 3D Fourier parameter. The formula for the solution of the obtained system is derived by the matrix transformations. Finally, the electric and magnetic fields are computed by the inverse Fourier transform. Using this formula the computation of the electric and magnetic fields has been made for the case when the current is a polarized dipole.