物理学报2013，Vol.62Issue(2)：55-64,10.DOI:10.7498/aps.62.020301
二维泊松方程的遗传PSOR改进算法
An ameliorative algorithm of two-dimensional Poisson equation based on genetic parallel successive over-relaxation method
摘要
Abstract
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.关键词
泊松方程/遗传算法/并行超松弛迭代法/有限差分法Key words
poisson equation/ genetic algorithm/ parallel successive over-relaxation method/ finite difference method引用本文复制引用
彭武,何怡刚,方葛丰,樊晓腾..二维泊松方程的遗传PSOR改进算法[J].物理学报,2013,62(2):55-64,10.基金项目
国家杰出青年科学基金(批准号:50925727)、国家自然科学基金(批准号:60876022,61102039,51107034)、湖南省科技计划项目(批准号:2011J4,2011JK2023)、国防预研重大项目(批准号:C1120110004)、广东省教育部产学研计划(批准号:2009B090300196)和中央高校基本科研业务费资助的课题. （批准号:50925727）
