OPTIMAL DIFFERENCE SCHEMES FOR MAXWELL’S EQUATIONS IN SOLVING FORWARD PROBLEMS OF ELECTROMAGNETIC SOUNDINGS
A.F. Mastryukov, B.G. Mikhailenko
Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of the Russian Academy of Sciences, pr. Akademika Lavrent’eva 6, Novosibirsk, 630090, Russia
Keywords: Maxwell’s equations, electromagnetic waves, finite difference method, Laguerre method
Abstract
In this paper, the solution of two-dimensional Maxwell’s equations is considered using the Laguerre transform. Optimal parameters of the difference schemes for the equations are obtained and presented. Numerical values of these optimal parameters are given. Second-order difference schemes with the optimal parameters provide an accuracy of the solution of the equations that is comparable to the accuracy of the solution using fourth-order schemes. It is shown that, when using the Laguerre transform, the number of optimal parameters can be reduced compared to the Fourier transform. This reduction leads to a simplification of the difference scheme and a reduction in the amount of computation, i.e., to efficiency of the algorithm.
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