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Computational Mathematics and Modeling

, Volume 30, Issue 1, pp 55–67 | Cite as

Numerical Analysis of the Integral Equation Method for the Computation of the Electromagnetic Field in a Nonhomogeneous Medium

  • V. I. DmitrievEmail author
  • I. S. Barashkov
II. MATHEMATICAL MODELING
  • 5 Downloads

The article considers mathematical modeling of the electromagnetic field in a nonhomogeneous medium by the integral equation method. The case of high-contrast conducting media is studied in detail, with the conducting nonhomogeneity embedded in a poorly conducting medium. The analysis of the integral equation, in this case, has shown that the solution deteriorates when the conducting nonhomogeneity is inside a low-conductivity layer. It is shown that this effect can be overcome by Dmitriev’s method of elevated background conductivity. The contrast effect is most pronounced for the H -polarized two-dimensional electromagnetic field in a nonhomogeneous medium. The numerical experiment has accordingly been conducted for this particular case. The solution computed by the integral equation method with elevated background conductivity is compared with the solution computed by the finite-difference method. The results of the two methods show excellent fit.

Keywords

electromagnetic sounding Maxwell equations nonhomogeneous medium integral equation method 

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References

  1. 1.
    V. I. Dmitriev, “Using the integral equation method in low-frequency electrodynamics of nonhomogeneous contrast media,” Prikl. Matem. Informat., No. 54, 50–56 (2017).Google Scholar
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    V. I. Dmitriev and E. V. Zakharov, Integral Equation Method in Computational Electrodynamics [in Russian], MAKS Press, Moscow (2008).Google Scholar
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    V. I. Dmitriev, Marine Electromagnetic Sounding [in Russian], Argamak Media, Moscow (2004).Google Scholar
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    V. I. Dmitriev, P. S. Belkin, and N. A. Mershchikova, “Integral equation method in the modeling of two-dimensional problems of geoelectrics,” Prikl. Matem. Informat., No. 18, 5–16 (2004).Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Computational Mathematics and CyberneticsMoscow State UniversityMoscowRussia

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