MSC2020 35K51
Development of a parallel algorithm based on an implicit scheme for the discontinuous Galerkin method for solving diffusion type equations
R. V. Zhalnin1, N. A. Kuzmin2, V. F. Masyagin3
| Annotation | 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. |
|---|---|
| Keywords | parabolic equations, discontinuous Galerkin method, implicit scheme, Nvidia AmgX |
1Ruslan V. Zhalnin, Head of Department of Applied Mathematics, Differential Equations and Theoretical Mechanics, National Research Mordovia State University (68/1 Bolshevistskaya St., Saransk 430005, Russia), Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0002-1103-3321, zhrv@mrsu.ru
2Nikita A. Kuzmin, student, Faculty of Mathematics and Information Technology, National Research Mordovia State University (68/1 Bolshevistskaya St., Saransk 430005, Russia), h0las@outlook.com
3Victor F. Masyagin, Senior Researcher, National Research Mordovia State University (68/1 Bolshevistskaya St., Saransk 430005, Russia), Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0001-6738-8183, masyaginvf@mrsu.ru
Citation: R. V. Zhalnin, N. A. Kuzmin, V. F. Masyagin, "[Development of a parallel algorithm based on an implicit scheme for the discontinuous Galerkin method for solving diffusion type equations]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,22:1 (2020) 94–106 (In Russian)
DOI 10.15507/2079-6900.22.202001.94-106
