对Braess方法的一点备注

SOME REMARKS ON BRAESS METHOD

Dictrich Braess针对网络比为2^(1/2)的棋盘形网格提出了种一多网格算法.这种算法较传统的多网格方法不同的是在校正前后分别加了一个半步G-S迭代作为转换步.本文对原算法稍作了修改,减少了工作量,并对修改后的算法给出了收敛性的理论证明.数值例子还表明比原算法有更好的收敛性效果。

Dictrich Braess puts forward a special multigrid method onthe chessboard mesh where the ratio of mesh sizes is 2^(1/2).This methoddiffers from classical multigrids on one additional step which is so-called half step G-S iteration before the coarse mesh correction and thesame one after it.This paper manages to improve Braess method anddecrease its computational works. Both theoretical proves and practicalexperiment have tested the superiority of the refovmed Braess method.