On the Application of Mosaic-Skeleton Approximations of Matrices in Electrodynamics Problems with Impedance Boundary Conditions - Setukha, A. V.; Stavtsev, S. L. (Lobachevskii journal of mathematics, 2023)
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.