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首页> 外文会议>Finite difference methods: theory and applications >Solving a Singularly Perturbed Elliptic Problem by a Cascadic Multigrid Algorithm with Richardson Extrapolation
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Solving a Singularly Perturbed Elliptic Problem by a Cascadic Multigrid Algorithm with Richardson Extrapolation

机译：用Richardson外推的级联多重网格算法求解奇摄动椭圆问题

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摘要

A two-dimensional linear elliptic equation with regular boundary layers is considered in the unit square. It is solved by using an upwind difference scheme on the Shishkin mesh which converges uniformly with respect to a small parameter ε. It is known that the application of multigrid methods leads to essential reduction of arithmetical operations amount. Earlier we investigated the cascadic two-grid method with the application of Richardson extrapolation to increase the e-uniform accuracy of the difference scheme. In this paper multigrid algorithm of the same structure is studied. We construct an extrapolation of initial guess using numerical solutions on two coarse meshes to reduce the arithmetical operations amount. The application of the Richardson extrapolation method based on numerical solutions on the last three meshes leads to increase the e-uniform accuracy of the difference scheme by two orders. The different components of a cascadic multigrid method are studied. The results of some numerical experiments are discussed.
机译：在单位正方形中考虑具有规则边界层的二维线性椭圆方程。通过在Shishkin网格上使用迎风差分方案解决该问题，该方案相对于小参数ε均匀收敛。众所周知，多网格方法的应用导致算术运算量的本质减少。先前我们使用Richardson外推法研究级联两网格方法，以提高差分方案的电子均匀精度。本文研究了相同结构的多重网格算法。我们使用两个粗糙网格上的数值解来构造初始猜测的外推法，以减少算术运算量。基于数值解的Richardson外推方法在最后三个网格上的应用导致差分方案的电子均匀精度提高了两个数量级。研究了级联多重网格方法的不同组成部分。讨论了一些数值实验的结果。

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