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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 5, Pages 878–884
DOI: https://doi.org/10.31857/S0044466921050161 (Mi zvmmf11243) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Partial Differential Equations

Numerical method for solving volume integral equations on a nonuniform grid

A. B. Samokhina, E. E. Tyrtyshnikovb

a Russian Technological University MIREA, 119454, Moscow, Russia
b Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333, Moscow, Russia
Citations (3)
DOI: https://doi.org/10.31857/S0044466921050161
Abstract: Numerical methods for solving volume integral equations describing the problems of wave scattering by transparent obstacles are considered. The equations are approximated using the collocation method on a nonuniform grid, and the problem is reduced to solving a system of linear algebraic equations. An efficient method is proposed for the approximate multiplication of the matrix of this system by a vector, which is comparable in complexity to the method used in the case of a uniform grid. An auxiliary uniform grid is introduced, and methods of interpolation of functions and algorithms of the fast discrete Fourier transform are used. It is essential that the number of nodes of the auxiliary uniform grid is comparable to the number of nodes of the original nonuniform grid.
Key words: volume integral equations, collocation method, nonuniform grid, methods for interpolation of functions, efficient algorithms.
Funding agency Grant number
Moscow Center of Fundamental and Applied Mathematics 075-15-2019-1624
This work was supported by the Moscow Center for Fundamental and Applied Mathematics (agreement no. 075-15-2019-1624 with the Ministry of Education and Science of the Russian Federation).
Received: 24.12.2020
Revised: 24.12.2020
Accepted: 14.01.2021
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 5, Pages 847–853
DOI: https://doi.org/10.1134/S0965542521050158
Bibliographic databases:
Document Type: Article
UDC: 517.63
Language: Russian
Citation: A. B. Samokhin, E. E. Tyrtyshnikov, “Numerical method for solving volume integral equations on a nonuniform grid”, Zh. Vychisl. Mat. Mat. Fiz., 61:5 (2021), 878–884; Comput. Math. Math. Phys., 61:5 (2021), 847–853
Citation in format AMSBIB
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    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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