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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Vydáno v:Lobachevskii journal of mathematics Ročník 44; číslo 9; s. 4062 - 4069
Hlavní autoři: Setukha, A. V., Stavtsev, S. L.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Moscow Pleiades Publishing 01.09.2023
Témata:
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
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Popis
Shrnutí: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