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

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.