Parallelization of 2-D IADE-DY Scheme on Geranium Cadcam Cluster for Heat Equation

Abstract

A parallel implementation of the Iterative Alternating Direction Explicit method by D’Yakonov (IADE-DY) for solving 2-D heat equation on a distributed system of Geranium Cadcam cluster (GCC) using the Message Passing Interface (MPI) is presented. The implementation of the scheduling of n tri-diagonal system of equations with the above method was used to show improvement on speedup, effectiveness, and efficiency. The Master/Worker paradigm and Single Program Multiple Data (SPMD) model is employed to manage the whole computation based on the use of domain decomposition. The completion of the execution can need task recovery and favorable configuration. The above mentioned details consist of a main report about the numerical validation of the parallelization through simulation to demonstrate the proposed method effectiveness on the cluster system. It was found that the rate of convergence decreases as the number of processors increases. The result of this paper suggests that the 2-D IADE-DY scheme is a good approach to solving problems, particularly when it is simulation with more processors.