Multigrid methods for elliptic problems in unbounded domains
Multigrid methods for elliptic problems in unbounded domains
复制标题
无界域椭圆问题的多重网格方法
DOI：
10.1137/0730008
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发表时间：
1993
影响因子：
2.9
通讯作者：
C. Goldstein
中科院分区：
文献类型：
--
作者：
C. Goldstein
本文的目的是研究多重网格方法在有界区域外求解椭圆问题的数值解。数值方法由一个截断的区域上的直径R和施加一个简单的局部近似边界条件的外边界上的原始问题。由此产生的问题是离散使用有限元法。R必须足够大，以将截断误差（由于近似边界条件）降低到离散化误差的水平。当使用准均匀网格时，这会导致非常大量的未知数（在三维中增加如$0（R^3）$）。在以前的工作由作者[数学。36（1981），pp. 387-404]，它表明，最佳误差估计与未知数的数量无关的R使用网格分级程序，其中的元素的大小是系统地增加，因为它们从原点的距离增加。
The goal of this work is to study multigrid methods in connection with the numerical solution of elliptic problems in the exterior of a bounded domain. The numerical method consists of approximating the original problem by one on a truncated domain of diameter R and imposing a simple local approximate boundary condition on the outer boundary. The resulting problem is discretized using the finite element method. R must be made sufficiently large to reduce the truncation error (due to the approximate boundary condition) to the level of the discretization error. This results in a very large number of unknowns (increasing like $0(R^3 )$ in three dimensions), when a quasi-uniform mesh is used. In previous work by the author [Math. Comp., 36 (1981), pp. 387–404], it was shown that optimal error estimates hold with the number of unknowns independent of R using a mesh grading procedure in which the size of the elements are systematically increased as their distance from the origin increases.In the present paper i...