A Parallel PCG Solver Based on OpenMP for Three-dimensional Heat Equation

Heat equation has been widely used in engineering, such as numerical simulation of groundwater flow. The parallelization of heat equation is an important means of accelerating the simulation process. In order to solve the three-dimensional heat equation problem more rapidly, the OpenMP was adopted to parallelize the preconditioned conjugate gradient (PCG) algorithm in this paper. A numerical experiment on the three-dimensional heat equation model was carried out on a computer with four cores. Based on the test results, it is found that the execution time of the original serial PCG program is about 1.71 to 2.81 times of the parallel PCG program executed with different number of threads. The experiment results also demonstrate that using OpenMP to parallelize the PCG algorithm is an effective way for solving the three-dimensional heat equation.