外推瀑布多网格法(EXCMG)——大规模求解椭圆问题的新算法  

EXTRAPOLATION CASCADIC MULTIGRID METHOD (EXCMG)—A NEW ALGORITHM FOR SOLVING LARGE SCALE ELLIPTIC PROBLEMS

作　　者：胡宏伶[1] 陈传淼[1] 谢资清[1] 

机构地区：[1]湖南师范大学数学与计算机学院,长沙410081

出　　处：《计算数学》2009年第3期261-274,共14页Mathematica Numerica Sinica

基　　金：国家自然科学基金(No.10771063);国家教育部博士点基金(No.20050542006)资助项目

摘　　要：基于有限元的渐近展开式,导出了新的外推公式,它们更精确地逼近密网上的有限元解(而不是微分方程的解),提出了新的外推瀑布型多网格法(EXCMG),采用新外推公式及其二次插值提供密网上的好初值,数值实验表明,新方法有很高的精度和效率.最后在PC机上求解了大规模二维椭圆问题。Based on an asymptotic expansion of finite element solution, some new extrapolation formulas are derived, which are the exacter approximations to the finite element solution on refined grid （rather than the solution of partial differential equation）. A new extrapolation cascadic multigrid method（EXCMG） is proposed based on the better initial values on refined grid provided by the new extrapolation formulas and their quadratic interpolation. The numerical experiments show that the new algorithm is of the high accuracy and efficiency. Finally a large scale elliptic problem of second order is solved in PC.

关 键 词：瀑布多网格法 有限元 新外推公式 二次插值 大规模 椭圆问题 

分 类 号：O241.82[理学—计算数学] TP301.6[理学—数学]