On the parallel iterative finite difference algorithm for 2-D Poisson's equation with MPI cluster

In this paper, a parallel iterative finite difference method (PIFD) for solving 2D Poisson's equation on a distributed system using Message Passing Interface (MPI) is investigated. This method is based on the domain decomposition method, where the 2D domain is divided into multiple sub-domains using horizontal and/or vertical axis depending on the available number of computer nodes. For interior points Poisson's equation is solved implicitly by four iterative schemes in combining with the boundary conditions. At the interface points of interior subdomains, Poisson's equation is solved by explicit iterative schemes. The proposed approach fulfills the suitability for the implementation on Linux PC cluster through the minimization of inter-process communication by restricting the exchange of data to the interface between the sub-domains. To examine the efficiency and accuracy of the iterative algorithm, several numerical experiments using different number of nodes of the Linux PC cluster are tested. The performance metrics clearly show the benefit of using the proposed approach on the Linux PC cluster in terms of execution time reduction and speedup with respect to the sequential running in a single PC.