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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2025 Volume 65, Number 7, Pages 1178–1195 (Mi zvmmf12011)

General numerical methods

Application of the mosaic-skeleton matrix approximation method in electromagnetic scattering problems

A. V. Setukhaab, S. L. Stavtsevb, S. N. Fetisovc, A. N. Mukhinc

a Lomonosov Moscow State University
b Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow
c Lyulka Design Bureau, UEC Ufa Engine-Building Industrial Group branch, Moscow

Abstract: The paper considers algorithms for solving problems of electromagnetic wave scattering in the frequency domain using the method of integral equations, as well as using the physical optics model taking into account a multiple reflected field. In both cases, the main computational costs, both in terms of computation time and in terms of the required computer memory, are associated with storing dense matrices of interaction of discrete elements and performing operations with these matrices. The features of applying the method of mosaic-skeleton approximations to such matrices, and the capabilities of this method in this class of problems are analyzed.

Key words: numerical methods, low-rank approximations, electromagnetic scattering, integral equations, physical optics method.

UDC: 519.642

Received: 28.04.2025
Accepted: 30.04.2025

DOI: 10.31857/S0044466925070083


 English version:
Computational Mathematics and Mathematical Physics, 2025, 65:7, 1691–1708

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© Steklov Math. Inst. of RAS, 2025