On the order of prolongations and restrictions in multigrid procedures
On the order of prolongations and restrictions in multigrid procedures
复制标题
DOI：
10.1016/0377-0427(90)90047-4
复制
发表时间：
1990-11
影响因子：
2.4
通讯作者：
P. Hemker
中科院分区：
文献类型：
--
作者：
P. Hemker
在多重网格法中，延拓的阶数和约束的阶数应满足一定的条件。一个经验法则是，延长和限制的阶数之和应该至少等于解出的微分方程的阶数。在本文中，我们证明了这一规则的正确性。我们注意到，我们必须区分低频和高频阶的转移算子。对于约束，低频阶数与其精度有关，而对于插值算子，两个阶数都与插值结果的精度有关。如果一个插值规则使得所有k − 1阶的多项式不变，那么低频阶和高频阶都等于k。在上述经验法则中起作用的是高频阶。
It is well known in the world of multigrid that the order of the prolongation and the order of the restriction in a multigrid method should satisfy certain conditions. A rule of thumb is that the sum of the orders of the prolongation and of the restriction should at least be equal to the order of the differential equation solved. In this note we show the correctness of this rule. We notice that we have to distinguish between low frequency and high frequency orders for the transfer operators. For the restriction, the low frequency order is related with its accuracy, whereas for the interpolation operator both orders are related with the accuracy of the result of the interpolation. If an interpolation rule leaves all polynomials of degreek− 1 invariant, then both the low and the high frequency order are equal tok. It is the high frequency order that plays a role in the above-mentioned rule of thumb.