Optimized parallel algorithm for solving the Poisson equation in non-stationary problems

We compare two algorithms for solving the Poisson equation: the first one is based on domain decomposition with direct coupling of subdomains (DDCS) and the second one is based on multidimensional Fast Fourier Transform and data transposition (FFTT).

Results of the comparison made helped us to introduce several optimizations for the DDCS method and to develop a new method combining DDCS/FFTT, that is aimed at solving the 3D Poisson equation on grids with billions of nodes using thousands of processors.