二维泊松方程的遗传PSOR改进算法

针对二维泊松方程在实际应用过程中几种常用方法存在计算量大、易发散、局部收敛等不足,提出了一种改进算法.该算法基于并行超松弛迭代法,采用遗传算法对松弛因子进行全局寻优,解决了超松弛迭代法求解泊松方程时最佳松弛因子难以确定的问题.构建了多目标适应度函数,优化了遗传算子参数,分析了算法的计算量、计算时间与误差精度,与传统方法进行了对比研究.结果表明:松弛因子对泊松方程求解的速度与精度影响显著;改进算法能减少迭代次数,节省计算时间,加快方程的求解;算法适合于求解计算量较大、精度要求较高的时域有限差分方程,而且精度要求越高,算法的性能越好,节省的时间也越多.

An ameliorative algorithm of two-dimensional Poisson equation based on genetic parallel successive over-relaxation method

There exist some disadvantages in the calculation of two-dimensional Poisson equation with several common methods. A new ameliorative algorithm is presented. It is based on a parallel successive over-relaxation (PSOR) method, by using the multi-objective genetic algorithm to search for optimal relaxation factor, with which the problem of optimal relaxation factor selection in PSOR is solved. The multi-objective fitness function is constructed, with which the genetic algorithm parameters are optimized. The analysis mainly focuses on algorithm computation, time cost and accuracy of error correction. The performance of the ameliorative algorithm is compared with those of Jacobi, Gauss-Seidel, Successive over relaxation iteration (SOR) and PSOR. Experimental results show that relaxation factor has a significant effect on the speed of solving Poisson equation, as well as the accuracy. The improved algorithm can increase the speed of iteration and obtain higher accuracy than traditional algorithm. It is suited for solving complicated finite difference time domain equations which need high accuracy. The higher the accuracy requirement, the better the performance of the algorithm is and the more computation time can also be saved.