The parallelization of the direct and iterative schemes for solving boundary layer problem on heterogeneous cluster systems

Abstract

In this paper, we present iterative schemes, specifically the iterative schemes: conjugate gradient, and Gauss-Seidel as well as direct schemes: LU factorization and Gauss elimination for solving boundary layer problem. The aim of this paper is to offer reasonable assessments and contrasts on behalf of the numerical experiments of these two schemes. The sequential and parallel programming is developed using a C programming language under Linux environment, while the parallel programming is running using the Parallel Virtual Machine (PVM) on a heterogeneous cluster systems. The analysis of the results are conducted in terms of numerical and parallel performance evaluations namely execution time, speedup, efficiency, effectiveness and temporal performance. The results prove that the iterative methods of conjugate gradient and Gauss-Seidel method are the alternatives scheme for solving the large scale computation.