Parallel Preconditioned Conjugate Gradient Method For A Three-Dimensional Heat Equation Based On OpenMP

The purpose of this study was to identify an efficient way of boosting computing power during solving large scale engineering problems using appropriate parallel methods. Engineering problems are considered to be relatively large and processing such problem will always require a large amount of processing time or rather execution time. The system based on a single computer can not solve these problems that need massive computation because it can not meet the demand of memory requirement. This research has been focusing on specific engineering problem referred to as the heat equation. The heat equation has widely been used in engineering related problems. Specifically, it is used in the simulation of ground water flow. Therefore this research focuses on identifying parallel numerical methods for parallelizing this large scale problem. The parallelization of the heat equation is an important means of accelerating the simulation process. In order to solve the three dimensional heat equation problems more rapidly and produce more efficient results, the OpenMP was adopted to parallelize the preconditioned conjugate gradient (PCG) algorithm in this research.Four numerical experiments on the three dimensional heat equation models were carried out on a computer that is running on a four cores processor. These four models were the discretized 50*50*120, 100*100*120, 150*150*120 and 300*300*120 spatial grids by the finite difference method. According to the results obtained, it has been observed that the execution time for the original serial PCG program is about 1.530 to 2.129 times of the parallel PCG program executed with different threads as an average to all the four experimental models used in this research. The experiment results also demonstrate that using OpenMP to parallelize the PCG algorithm is an effective way for solving the three-dimensional heat equation.