Optimal parallel algorithm of calculation of points of a computational front hyperplane and its comparison with other iteration methods of solving of grid equations

This paper offers an algorithm of calculation of points of a computational front hyper plane, optimal for parallelization, including CUDA GPUs. In the second part of the paper, different methods of solving of systems of linear equations are compared from the viewpoint of efficiency on example of Poisson's equation (heat conductivity task). Besides explicit (Jacobi method) and implicit (Gauss–Seidel methods) schemes, the paper also considers two-level simple iteration method, two and three-level Chebyshev methods and multi grid method. Gauss–Seidel methods were also considered together with successive over relaxation (SOR) method. All algorithms were implemented in serial version and in parallel version on CUDA GPUs. To simplify transformation on CUDA, gridmath library was utilized.