Implementation and performance analysis of sequential versus parallelized algorithms for solving multivariate equations of CFD Poisson processes

The present work aims to find computationally-efficient models for solving discretized partial differential equations. To accomplish that, we implement and compare the performance of a series of algorithmic models, both sequential and parallelized (using OpenMP libraries), which may be used for solving convergence problems. For demonstrating the results upon a real-world case scenario, the work introduces a CFD (computational fluid dynamics) Poisson process, which is numerically discretized and approximated using Jacobi and Gauss-Seidel algorithms. Performance of the parallelized implementations will be measured against a baseline, and the consequent model optimizations will be described. Finally, the scalability of the parallelized algorithms will be compared together, with regards to CPU thread count and memory handling. The results show that, compared with a sequential version, a parallelized Jacobi algorithm shows strong performance and scalability when introducing more threads. At the same time, a parallelized version of the Gauss-Seidel algorithm did not present substantial increases in performance over its sequential counterpart.