五点差分格式求解泊松方程并行算法的研究

Parallel Algorithm Research on Solving Poisson Equations Based on Five Point Difference Format

摘要: 以二维静电场泊松方程数值求解的串行算法(雅可比迭代、超松弛迭代)为基础,提出了五点差分格式超松弛迭代(SOR)求解二维静电场泊松方程的并行算法,通过与雅可比迭代(Jacobi)并行算法的时间复杂度、加速比和空间复杂度进行对比,得出超松弛迭代的并行算法具有更低的时间复杂度、空间复杂度和更高的加速比与效率。通过实验验证,CHIPIC软件的泊松模块宜采用超松弛迭代并行算法。

Abstract: In this paper, the efficiency of Jacobi iterative parallel algorithm for solving 2D Poisson equation is analyzed, and then the design of successive over relaxation (SOR) iterative parallel algorithm is presented. The result shows that SOR iterative parallel algorithm should be adopted in developing CHIPIC Poisson module by comparing the time complexity, speedup, and space complexity of the two algorithms in theory. At last, the result is verified by numerical experiment.