IMPLEMENTING JACOBI ALGORITHM VERSUS GAUSS-SEIDEL ALGORITHM IN SOLVING A DISCRETIZED PROBLEM

As it is well known that performance of algorithms generally relies both on the hardware that they are run on and on the way that they are implemented and executed the present paper aims to show that the executions’ wall-clock time might be affected by parallelizing the code, although this could sometimes become a hard task. Within this work, based on Poisson partial differential equation, we shall present different aspects of a comparison between implementing Jacobi algorithm in solving a discretized problem and implementing Gauss-Seidel algorithm in solving the same. On one hand, the results obtained by implementing the Jacobi algorithm benefited very much from the parallelization, so the first case has shown both good performance and scalability when introducing supplementary threads; as its structure always needed to exhibit a complete data copy computed in its former iterations, it became easier for us to have the code parallelly executed, because there was an insignificant risk of data races’ hitting. On the other hand, the results obtained by implementing the Gauss-Seidel algorithm managed to solve the discretized problem, although its performance was not as good as the one of the Jacobi algorithm, so the second case has shown a good execution performance in varying sizes of sequentially executed data, taking into account that, as far as parallelizing was concerned, the performance was unreliable and random.