M. A. Sultanov a,b), E. N. Akimova 1,c,d), V. E. Misilov c,d), B. T. Sarsenov a,b), Y. Nurlanuly a,b)
a) Institute of Mathematics and Mathematical Modeling, Pushkin Street 125, Almaty 050010, Kazakhstan
b) Department of Mathematics, Faculty of Natural Science, Khoja Akhmet Yassawi International Kazakh-Turkish University, B. Sattarhanov Street 29, Turkestan 160200, Kazakhstan
c) Krasovskii Institute of Mathematics and Mechanics, S. Kovalevskaya Street 16, Ekaterinburg 620077, Russia
d) Institute of Radioelectronics and Information Technology, Ural Federal University, Mira Street 19, Ekaterinburg 620002, Russia
Received October, 2025; accepted in revised form October, 2025
Abstract: This work is devoted to the construction of efficient parallel algorithms and development of parallel code for solving the two-dimensional stationary elliptic differential equation. The numerical algorithm is based on a finite difference sc heme. After discretization and application of this scheme, we obtain a large system of linear algebraic equations with a block-tridiagonal matrix. To solve this equation, we apply the matrix sweep method.
In this work, we have developed a parallel code for graphics processors using the CUDA technology and cuBLAS and cuSOLVER libraries. We have achieved a 5-fold speedup in comparison with the earlier CPU code.
© 2025 European Society of Computational Methods in Sciences and Engineering
Keywords: Partial differential equation; elliptic problem; finite difference scheme, matrix sweep method, CUDA
Mathematics Subject Classification: 35J25; 65Y05
PACS: 02.30.Jr; 02.60.Lj