自共轭椭圆偏微分方程的m-step Jacobi PCG方法

The m-step Jacobi PCG method for the self-conjugate elliptic partial differential equations

M stepJacobi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。

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 is more effective than the odd steps one. Specially,the more steps, the faster the convergence velocity.