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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2020, Volume 60, Number 7, Pages 1095–1110
DOI: https://doi.org/10.31857/S004446692007011X
(Mi zvmmf11098)
 

This article is cited in 2 scientific papers (total in 2 papers)

Quadrature formulas of Gauss type for a sphere with nodes characterized by regular prism symmetry

A. M. Voloshchenko, A. A. Russkov

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047 Russia
Citations (2)
References:
Abstract: When the transport equation is solved by the discrete ordinate method, the problem arises of constructing quadrature formulas on a sphere characterized by the required accuracy and making it possible to use the quadrature nodes to approximate the transport equation in $r, \vartheta,z$ geometry, in which quadrature nodes are simultaneously used to approximate the derivative with respect to the azimuth angle $\varphi$ of the transport equation, that is, must be located in levels on the sphere with the same values of the polar angle $\theta$. An algorithm is considered to construct quadrature formulas of the needed form that are characterized by regular prism (dihedron) symmetry and exact for all spherical polynomials of degree not exceeding some maximal value $L$. This study is a development of the work of A.N. Kazakov and V.I. Lebedev (1994). The constructed family of quadratures, unlike that in the above work, does not contain nodes with $\varphi=0,\pi/2,\pi ,3\pi/2$, at the poles $\theta=\pm\pi/2$, and on the equator $\theta=0$ of the sphere. It is shown that this family ensures a significant computational gain when radiation transport problems are solved in three-dimensional geometry.
Key words: Gauss-type quadratures on a sphere, transport equation.
Received: 17.02.2018
Revised: 09.01.2020
Accepted: 10.03.2020
English version:
Computational Mathematics and Mathematical Physics, 2020, Volume 60, Issue 7, Pages 1063–1077
DOI: https://doi.org/10.1134/S0965542520070118
Bibliographic databases:
Document Type: Article
UDC: 519.6:536.71
Language: Russian
Citation: A. M. Voloshchenko, A. A. Russkov, “Quadrature formulas of Gauss type for a sphere with nodes characterized by regular prism symmetry”, Zh. Vychisl. Mat. Mat. Fiz., 60:7 (2020), 1095–1110; Comput. Math. Math. Phys., 60:7 (2020), 1063–1077
Citation in format AMSBIB
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\vol 60
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\pages 1095--1110
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\crossref{https://doi.org/10.31857/S004446692007011X}
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