Effectiveness Evaluation of Parallel Execution of Some Mathematical Methods

Abstract

In many applications the essential part of the calculations in the programs are based on some well-known and defined mathematical method, such as FDM (Finite Difference Method), FEM (Finite Element Method), LU Factorization, SOR (successive over-relaxation) method, Monte Carlo method and so on. In such cases the decision how to execute effectively the application on a parallel machine should be taken according to the information how the appropriate mathematical method could be parallelized. Obviously it will be very convenient to have practical guidelines of how these methods perform in parallel versions on different parallel machines for a scale of input arguments. The following is a description of an attempt to receive representative figures for the behavior of two mathematical methods on three parallel machines.