Parallelization of Linear Iterative Methods for Solving the 3-D Pressure Poisson Equation Using Various Programming Languages

In this paper we explored parallelization of PPE (pressure Poisson equation) solvers with the aim of decreasing total arithmetic and run-time expenditure in incompressible CFD. For the current work, Jacobi and successive overrelaxation (SOR) iterations are used to solve this 3-D PPE, and they are parallelized with OpenMP employing programming languages Fortran, C and C++. Results show that parallelization greatly improves the serial calculation speed in general. Also it is found that 1) speedup increases sub-linearly with increasing number of cores; 2) parallelization efficiency first increases, and later decreases, as the problem size becomes larger; 3) Fortran is approximately 10% faster than C, and C is approximately 10% faster than C++ for serial cases; for parallel runs, Fortran shows little difference in execution time with C, but still is approximately 10% faster than C++. Comparisons are made in the context of having the same algorithm and code structure, and the same optimization level in compilation. Moreover, we found that optimal SOR is nearly two orders of magnitude faster than Jacobi iteration, both in serial and parallel modes, even for a very simple approach to SOR parallelization.