Development of a parallel algorithm based on an implicit scheme for the discontinuous Galerkin method for solving diffusion type equations

Autor:	Nikita A. Kuzmin, Ruslan V. Zhalnin, Victor F. Masyagin
Rok vydání:	2020
Předmět:	Scheme (programming language) Discontinuous Galerkin method Computer science MathematicsofComputing_NUMERICALANALYSIS Parallel algorithm Applied mathematics Development (differential geometry) computer Diffusion type computer.programming_language
Zdroj:	Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva. 22:94-106
ISSN:	2587-7496 2079-6900
DOI:	10.15507/2079-6900.22.202001.94-106
Popis:	The paper presents a numerical parallel algorithm based on an implicit scheme for the Galerkin method with discontinuous basis functions for solving diffusion-type equations on triangular grids. To apply the Galerkin method with discontinuous basis functions, the initial equation of parabolic type is transformed to a system of partial differential equations of the first order. To do this, auxiliary variables are introduced, which are the components of the gradient of the desired function. To store sparse matrices and vectors, the CSR format is used in this study. The resulting system is solved numerically using a parallel algorithm based on the Nvidia AmgX library. A numerical study is carried out on the example of solving two-dimensional test parabolic initial-boundary value problems. The presented numerical results show the effectiveness of the proposed algorithm for solving parabolic problems.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::7e1ea85606f65618b60fe919cc2c08db https://doi.org/10.15507/2079-6900.22.202001.94-106 Zobrazit plný text záznamu