An Extrapolation Cascadic MultigridMethod for Elliptic Problems on Reentrant Domains  

作　　者：Kejia Pan Dongdong He Chuanmiao Chen 

机构地区：[1]School of Mathematics and Statistics,Central South University,Changsha,Hunan 410083,China [2]School of Aerospace Engineering and Applied Mechanics,Tongji University,Shanghai 200092,China [3]College of Mathematics and Computer Science,Key Laboratory of High Performance Computing and Stochastic Information Processing(Ministry of Education of China),Hunan Normal University,Changsha,Hunan 410081,China

出　　处：《Advances in Applied Mathematics and Mechanics》2017年第6期1347-1363,共17页应用数学与力学进展（英文）

基　　金：Kejia Pan was supported by the National Natural Science Foundation of China(Nos.41474103 and 41204082);the National High Technology Research and Development Program of China(No.2014AA06A602);the Natural Science Foundation of Hunan Province of China(No.2015JJ3148);Dongdong He was supported by the Fundamental Research Funds for the Central Universities,the National Natural Science Foundation of China(No.11402174);the Program for Young Excellent Talents at Tongji University(No.2013KJ012);the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry。

摘　　要：This paper proposes an extrapolation cascadic multigrid(EXCMG)method to solve elliptic problems in domains with reentrant corners.On a class ofλ-graded meshes,we derive some new extrapolation formulas to construct a high-order approximation to the finite element solution on the next finer mesh using the numerical solutions on two-level of grids(current and previous grids).Then,this high-order approximation is used as the initial guess to reduce computational cost of the conjugate gradient method.Recursive application of this idea results in the EXCMG method proposed in this paper.Finally,numerical results for a crack problem and an L-shaped problem are presented to verify the efficiency and effectiveness of the proposed EXCMG method.

关 键 词：Richardson extrapolation Cascadicmultigrid gradedmesh elliptic problems corner singularity 

分 类 号：O24[理学—计算数学]