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Russian Geology and Geophysics

2008 year, number 8

Numerical solution of Maxwell's equations for anisotropic media using the Laguerre transform

A.F. Mastryukov, B.G. Mikhailenko
Institute of Computing Mathematics and Mathematical Geophysics, Siberian Branch of the RAS, 6 prosp. Akad. Lavrentieva, Novosibirsk, 630090, Russia
Keywords: Maxwell's equations; electromagnetic waves; anisotropic media; relaxation time; conductivity; dielectric permittivity; Laguerre transform; finite-difference time-domain method; linear equation system
Pages: 621-627


We apply the spectral Laguerre transform in the time domain to solve 2D Maxwell's equations for propagation of electromagnetic waves in lossy anisotropic media. The new algorithm is simple and efficient as Maxwell's equations are reduced to a harmonic series of linear algebraic equations where the matrix is independent of the harmonic order and is the same for all harmonics.
The efficiency of the algorithm is improved by fitting a specially introduced free parameter of the Laguerre transform. If it is large, the solution spectrum shifts toward higher harmonics which is formally equivalent to the case of ray approximation.
The Laguerre solution is comparable with high-order accurate finite-difference time-domain (FDTD) solutions. The method is stable both in the region of the wavefield, where conductivity approaches zero and the spectral Fourier method is unstable, and in the high-conductivity region, where the explicit FDTD code requires a too small time step.