椭圆型方程边值问题的拟多重网格预处理迭代法

Quasi Multigrid Preconditioned Iteration Method for Boundary Value Problem of Elliptic Equations

利用多重网格法的思想,构造出一种求解椭圆型方程边值问题的预处理迭代格式,并给出了收敛性证明.特别地,对常系数方程得到了收敛速度与网格步长无关的最优结果.数值实验表明,所构造方法收敛速度较SOR法有显著提高,其迭代次数几乎与网格步长无关,迭代解逼近精确解的精度高而且稳定.

By use of multigrid method, this paper proposes a preconditioned iteration method solving the boundary value problem of elliptic equations, the proof of convergence is given. Especially, the optimal result that the convergence rate is independent of mesh-size is presented for the elliptic equation with constant coefficients. The numerical results show the convergence rate of the given method is much faster than that of SOR method, and the number of iterations has almost no relation to the mesh-size. The iteration solution approximates the exact solution exactly and stably.