二维椭圆问题的经济外推瀑布多重网格法  

Economical Extrapolation Cascadic Multigrid Method for the Two-Dimensional Elliptic Problem

作　　者：李明[1] 赵金娥[1] 

机构地区：[1]红河学院数学学院,云南蒙自661199

出　　处：《西南大学学报（自然科学版）》2014年第7期68-72,共5页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11161014);云南省教育厅科研基金资助项目(2012C121);云南省科技厅青年项目(2012FD054)

摘　　要：针对二维椭圆问题,首先提出九点紧致中心差分(NCCD)格式,并讨论该格式的截断误差.接着,提出了基于NCCD格式下的经济外推瀑布多重网格(EEXCMG)法,其中使用新外推公式和三次多项式插值算子给相邻细网格层提供初始值,并在各网格层上采用经济的磨光策略.数值实验验证了NCCD格式的四阶精度和EEXCMG法的有效性.Firstly, a nine-point compact center different （NCCD） formula of the two-dimensional elliptic problem is constructed, and the truncation error of the formula is discussed. Secondly, based on the new different formula, an economical extrapolation cascadic multigrid （EEXCMG） method is proposed, in which the new extrapolation formula and cubic interpolation operator are used to provide a better initial value on the finer grids and an economical smoothing strategy is applied on those grids. The results of a numerical experiment demonstrate that the NCCD formula can obtain fourth order accuracy and the EEXC- MG method is effective.

关 键 词：紧致中心差分格式 新外推公式 经济的磨光策略 经济外推瀑布多重网格法 

分 类 号：O241.8[理学—计算数学]