Performance analysis of parallel virtual machine in solving large-scale multi-dimensional problems

Abstract

MATLAB Distributed Computing Server (MDCS) and Parallel Virtual Machine (PVM) software are two types of distributed computing environments. MDCS is recently used in selecting the best network training algorithm and assessing the effect of parallelization. Since it is practical and user friendly, it gives PVM the opportunity to become the communication paradigm of choice. The PVM provides a powerful set of process control and dynamic resource management features. In the distributed parallel computing (DPC), however, both solutions have different strengths and limitations. Based on these concerns, this paper compares the numerical analysis for mathematical modeling of large sparse 2D and 3D of second order parabolic partial differential equations (PDE) on MDCS and PVM based on parallel performance indicators (PPI). The PDE geometry is discretized into a sparse grid structure using the FDM method. In using a method with the highest accuracy, Parallel Alternating Group Explicit (PAGE) scheme was chosen. The parallel strategies focus on the PAGE's convergence speed and various domain de-composition techniques, as well as a block iterative scheme and load balance using fine granular techniques. Furthermore, comparison of distributed computing environments also relies on multiple processors running on Unix-like operating systems with Fedora installed to support large-scale simulations. The analysis and validation of PPI for both communication software is also investigated in this paper. For a sequential algorithm, accuracy, estimation of error, and stability are employed as indicators. As a conclusion, based on the PPI and numerical analysis, the tables and graphs show that compared to MDCS, PVM is a better environment for solving multidimensional parabolic PDE modeling.