On the Application of Mosaic-Skeleton Approximations of Matrices in Electrodynamics Problems with Impedance Boundary Conditions

A boundary value problem for Maxwell’s equations in the frequency domain with impedance boundary conditions is considered. The problem is reduced to solving a system of two boundary integral equations containing weakly and strongly singular integrals. For the numerical solution of a system of integr...

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Bibliographic Details
Published in:	Lobachevskii journal of mathematics Vol. 44; no. 9; pp. 4062 - 4069
Main Authors:	Setukha, A. V., Stavtsev, S. L.
Format:	Journal Article
Language:	English
Published:	Moscow Pleiades Publishing 01.09.2023
Subjects:	Algebra Analysis Geometry Mathematical Logic and Foundations Mathematics Mathematics and Statistics Probability Theory and Stochastic Processes integral equations impedance boundary condition fast matrix algorithms Maxwell’s equations
ISSN:	1995-0802, 1818-9962
Online Access:	Get full text
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Summary:	A boundary value problem for Maxwell’s equations in the frequency domain with impedance boundary conditions is considered. The problem is reduced to solving a system of two boundary integral equations containing weakly and strongly singular integrals. For the numerical solution of a system of integral equations, the paper presents a numerical solution method based on piecewise constant approximation and collocation methods. Thus, the original problem is reduced to solving a system of linear algebraic equations with a dense matrix. To effectively solve a system of linear equations, the method of mosaic-skeleton approximations of matrices is used. The specifics of applying the method of mosaic-skeleton approximations in this problem are analyzed.
ISSN:	1995-0802 1818-9962
DOI:	10.1134/S199508022309038X