自共轭椭圆偏微分方程的m-step Jacobi PCG方法

来源期刊：中南大学学报(自然科学版)2004年第2期

论文作者：向淑晃 彭小飞

文章页码：337 - 340

关键词：自共轭;共轭梯度;m步雅可比预处理

Key words：self-conjugate; conjugate gradient;m-step Jacobi preconditioning

摘    要：M-step Jacobi预处理共轭梯度法被用于求解源于自共轭椭圆偏微分方程的有限元或有限差分逼近的大型稀疏线性系统。这种方法的应用基础是相应的Jacobi迭代收敛。研究结果表明:偶数步的Jacobi预处理共轭梯度法较相邻奇数步的Jacobi预处理共轭梯度法更有效,步数越多,收敛速度越快。

Abstract: The m-step Jacobi PCG method is applied to solve the large sparse linear systems resulting from finite element or finite difference approximations of the self-conjugate elliptic partial differential equations.The method is based on assuming that Jacobi iteration is convergent. The results show that the even steps Jacobi PCG method ismore effective than the odd steps one. Specially,the more steps, the fasterthe convergence velocity.