Development of a hybrid parallel algorithm (MPI + OpenMP) for solving the Poisson equation

This article presents the development of a hybrid parallel algorithm for solving the Dirichlet problem for the two-dimensional Poisson equation. MPI and OpenMP were chosen as the technology for parallelization. For the numerical sequential solution of the Poisson equation, an explicit “cross” scheme was used (the Jacobi iterative method). A parallel algorithm was implemented by the method of decomposition of regions, namely, one-dimensional decomposition. In the article in the form of tables and graphs shows the acceleration and efficiency of parallel algorithms using MPI and OpenMP technologies separately and were compared with the acceleration and efficiency of the MPI + OpenMP hybrid algorithm. Also, the choice of the hybrid program architecture is justified and the distribution of data between processes is explained. The results show the effectiveness of using a hybrid algorithm for solving such problems and show the acceleration of time by 1.5-2 times. The presented algorithm was tested on a cluster of the computing center of the Novosibirsk State University for a different number of points in the computational domain (from 64x64 to 1024x1024). The results of the presented work can be applied to the simulation of problems of hydrodynamics, ecology, aerodynamics, the spread of chemical reagents, the propagation of heat and other physical processes