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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 5, Pages 917–932 (Mi zvmmf11085)  

Parallel mosaic-skeleton algorithm for the numerical solution of a three-dimensional scalar scattering problem in integral form

A. A. Kashirin, S. I. Smagin, M. Yu. Timofeenko

Computing Center, Far Eastern Branch, Russian Academy of Sciences, Khabarovsk, 680000 Russia

Abstract: A three-dimensional scalar stationary scattering problem is considered. It is formulated in the form of a weakly singular Fredholm boundary integral equation of the first kind with a single unknown function. The equation is approximated by a system of linear algebraic equations, which is then solved numerically by an iterative method. The mosaic-skeleton method is used at the stage of the approximate solution of this system in order to reduce the computational complexity of the approach.

Key words: scattering problem, integral equation, numerical solution, fast method, mosaic-skeleton method, incomplete cross approximation.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00682
20-01-00450
Ministry of Science and Higher Education of the Russian Federation 18-5-100
This work was supported by the Russian Foundation for Basic Research (project nos. 17-01-00682, 20-01-00450) and by the Far Eastern Branch of the Russian Academy of Sciences (basic research program, project no. 18-5-100).


DOI: https://doi.org/10.31857/S0044466920050099


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:5, 895–910

Bibliographic databases:

UDC: 519.642
Received: 11.05.2018
Revised: 11.09.2019
Accepted:14.01.2020

Citation: A. A. Kashirin, S. I. Smagin, M. Yu. Timofeenko, “Parallel mosaic-skeleton algorithm for the numerical solution of a three-dimensional scalar scattering problem in integral form”, Zh. Vychisl. Mat. Mat. Fiz., 60:5 (2020), 917–932; Comput. Math. Math. Phys., 60:5 (2020), 895–910

Citation in format AMSBIB
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\paper Parallel mosaic-skeleton algorithm for the numerical solution of a three-dimensional scalar scattering problem in integral form
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\pages 917--932
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