求解椭圆问题的一类外推三层网格法

使用线性拉格朗日有限元离散一类二维椭圆问题,选择合适剖分尺度形成最粗网格、次粗网格和最细网格和对应的方程组。在最粗网格和次粗网格上使用外推法（新外推法或经典外推法）得到次粗网格上高精度近似解,然后使用三次样条插值为细网格提供初始值,结合磨光算子,构造了经典外推三层网格法和新外推三层网格法,并给出相应的数值实验。与通常的瀑布型多重网格法相比,数值实验表明了两种新算法计算精度更高,细层上迭代步数非常少,计算时间更短,具有较强的稳健性。

A type of extrapolation three-level method for elliptic problem

The coarsest grid,coarse grid,finest grid and linear system of equations for two dimensional elliptic problem are given by apply linear Lagrange finite element,a better initial guess on coarse grid is given by using extrapolation formula（new extrapolation formula or classic extrapolation formula） on coarse grid and coarsest grid.Then a better initial value on finest grid is obtained by using cubic spline interpolation.A classic extrapolation three-level method and new extrapolation three-level method by combining with smooth operator are designed in this paper.Numerical experiment results show that the new methods are more efficient,comparing with usually cascadic multigrid method.