Dmitriev, V. I.; Silkin, A. N. Direct problem of calculating the magnetic dipole field in a quasilayered medium. (English. Russian original) Zbl 0938.78003 Comput. Math. Model. 10, No. 3, 291-306 (1999); translation from Chisl. Met. Mat. Fiz., Mosk. Gos. Univ. 1998, 94-110 (1998). Summary: A method is developed for calculating the electromagnetic field of a magnetic dipole in a quasilayered two-dimensional medium. The quasi-three-dimensional problem is reduced to a two-dimensional problem for the Fourier-transformed electromagnetic field. An equivalent system of integral equations on the layer boundaries is obtained. MSC: 78A25 Electromagnetic theory (general) 86A20 Potentials, prospecting 78M25 Numerical methods in optics (MSC2010) Keywords:electromagnetic sounding; efficient algorithm; electromagnetic field; magnetic dipole; quasilayered two-dimensional medium; integral equations Software:Maple PDFBibTeX XMLCite \textit{V. I. Dmitriev} and \textit{A. N. Silkin}, Comput. Math. Model. 10, No. 3, 1 (1998; Zbl 0938.78003); translation from Chisl. Met. Mat. Fiz., Mosk. Gos. Univ. 1998, 94--110 (1998) Full Text: DOI References: [1] P. L. Chebyshev,Collected Works [in Russian], USSR Academy of Sciences Press, Moscow/Leningrad (1944–1951). [2] I. S. Berezin and N. P. Zhidkov,Computational Methods, [in Russian], Fizmatgiz, Moscow (1959–1960). · Zbl 0096.09401 [3] E. Goursat,A Course of Mathematical Analysis, Dover, New York (1959–1964). · Zbl 0144.04501 [4] L. Collatz,Functional Analysis and Numerical Mathematics, Academic Press, New York (1966). · Zbl 0148.39002 [5] P. Gill, W. Murray, and M. Wright,Practical Optimization, Academic Press, New York (1981). · Zbl 0503.90062 [6] Yu. N. Kiselyov,Optimal Control [in Russian], Moscow University Press (1988). [7] Yu. N. Kiselyov, M. V. Orlov, and E. L. Fedotova, ”Projection of a point on an ellipsoid,”Vestn. Mosk. Univ., Ser. 15, No. 1, 45–50 (1993). [8] Y. N. Kiselev, ”Algorithms of projection of a point onto an ellipsoid,”Lith. Math. J. 34, No. 2, 141–159 (1994). · Zbl 0831.65062 [9] S. N. Avvakumov, Yu. N. Kiselyov, and M. V. Orlov, ”Methods of solving optimal control problems using the Pontryagin maximal principle,”Trud. Mat. Inst. Ross. Akad. Nauk,211, 3–31 (1995). [10] Bruce W. Char, Keith O. Geddes, Gaston H. Gonnet, Benton L. Leong, Michael B. Monogan, and Stephen M. Watt,Maple V Language Reference Manual, Springer-Verlag, New York (1991). · Zbl 0758.68038 [11] Bruce W. Char, Keith O. Geddes, Gaston H. Gonnet, Benton L. Leong, Michael B. Monogan, and Stephen M. Watt,First Leaves: ATutorial Introduction to Maple V, Springer-Verlag, New York (1992). · Zbl 0758.68037 [12] Yu. N. Kiselyov, ”Differentiability of the mapping that describes isochrone surfaces in the linear time optimization problem,”Differents. Uravn.,7, No. 8, 1385–1392 (1971). · Zbl 0222.49005 [13] Yu. N. Kiselyov ”Asymptotic solution of the time optimization problem under analytic perturbations of the initial conditions,”Differents. Uravn.,7, No. 12, 2151–2160 (1971). · Zbl 0225.49012 [14] Yu. N. Kiselyov, ”Computational formalism of the solution of the linear time optimization problem with regular perturbations,” in:Dynamics of Controllable Systems [in Russian], Nauka, Novosibirsk (1979), pp. 166–174. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.