In this paper, a parallel implementation of the Iterative Alternating Direction Explicit method by D'Yakonov (IADE-DY) to solve 2-D telegraphic problem on a distributed system using Message Passing Interface (MPI) and Parallel Virtue Machine (PVM) are presented. The parallelization of the program is implemented by a domain decomposition strategy. A Single Program Multiple Data (SPMD) model is employed for the implementation. The implementation is discussed in relation to means of the parallel performance strategies and analysis. The model enhances overlap communication and computation to avoid unnecessary synchronization, hence, the method yields significant speedup. The level of speedup observed from tables as the mesh increases are in the range of 5-10%. Improvement has been achieved by numbers of tables and figures in our experiment. We present some analyses that are helpful for speedup and efficiency. It is concluded that the efficiency is strongly dependent on the grid size, block numbers and the number of processors for both MPI and PVM. Different strategies to improve the computational efficiency are proposed.

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In this paper, a method based on applying Successive Over-Relaxation (SOR) to find the solution of 2-Dimensional Bio-Heat Transfer Problem (2DBHTP) on a distributed computing environment using Input File Affinity Measure (I aff) with Message Passing Interface (MPI) is introduced. A finite difference discretization is developed to solve the 2DBHTP since 2DBHTP requires the evaluation of temporal and spatial distributions of temperature. The platform gives us better predictions of the effects of thermal physical properties of temperature distribution. This work proposes a parallel overhead with overlapping communication in its implementation using MPI. Based on the implementation of the MPI distributed computing environment, we present a performance improvement strategy running on the master-slave platform. Parallel comparisons of the method were experimentally evaluated, and parallel results show speedup and efficiency on a various number of mesh sizes. The method used combines elements of numerical stability and parallel algorithm design.