Open AccessDevelopment of a parallel algorithm based on an implicit scheme for the discontinuous Galerkin method for solving diffusion type equations
Author(s) -
Ruslan V. Zhalnin,
Nikita A. Kuzmin,
V. F. Masyagin
Publication year - 2020
Publication title -
žurnal srednevolžskogo matematičeskogo obŝestva
Language(s) - English
Resource type - Journals
eISSN - 2587-7496
pISSN - 2079-6900
DOI - 10.15507/2079-6900.22.202001.94-106
Subject(s) - mathematics , discontinuous galerkin method , galerkin method , basis function , partial differential equation , scheme (mathematics) , boundary value problem , basis (linear algebra) , algorithm , numerical analysis , parabolic partial differential equation , function (biology) , mathematical analysis , finite element method , geometry , physics , evolutionary biology , biology , thermodynamics
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.