Geodesic
Development of a parallel algorithm based on an implicit scheme for the discontinuous Galerkin method for solving diffusion type equations
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 22 (2020) no. 1, pp. 94-106

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Mots-clés : parabolic equations, implicit scheme
Keywords: discontinuous Galerkin method, Nvidia AmgX. 
@article{SVMO_2020_22_1_a6,
     author = {R. V. Zhalnin and N. A. Kuzmin and V. F. Masyagin},
     title = {Development of a parallel algorithm based on an implicit scheme for the discontinuous {Galerkin} method for solving diffusion type equations},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {94--106},
     publisher = {mathdoc},
     volume = {22},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2020_22_1_a6/}
}
TY  - JOUR
AU  - R. V. Zhalnin
AU  - N. A. Kuzmin
AU  - V. F. Masyagin
TI  - Development of a parallel algorithm based on an implicit scheme for the discontinuous Galerkin method for solving diffusion type equations
JO  - Žurnal Srednevolžskogo matematičeskogo obŝestva
PY  - 2020
SP  - 94
EP  - 106
VL  - 22
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SVMO_2020_22_1_a6/
LA  - ru
ID  - SVMO_2020_22_1_a6
ER  - 
%0 Journal Article
%A R. V. Zhalnin
%A N. A. Kuzmin
%A V. F. Masyagin
%T Development of a parallel algorithm based on an implicit scheme for the discontinuous Galerkin method for solving diffusion type equations
%J Žurnal Srednevolžskogo matematičeskogo obŝestva
%D 2020
%P 94-106
%V 22
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SVMO_2020_22_1_a6/
%G ru
%F SVMO_2020_22_1_a6
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. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 22 (2020) no. 1, pp. 94-106. http://geodesic.mathdoc.fr/item/SVMO_2020_22_1_a6/