An Extrapolation Cascadic Multigrid Method for Elliptic Problems on Reentrant Domains

被引：6

作者：

Pan, Kejia ^{[1
]}

He, Dongdong ^{[2
]}

Chen, Chuanmiao ^{[3
]}

机构：

[1] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

[2] Tongji Univ, Sch Aerosp Engn & Appl Mech, Shanghai 200092, Peoples R China

[3] Hunan Normal Univ, Coll Math & Comp Sci, Key Lab High Performance Comp & Stochast Informat, Minist Educ China, Changsha 410081, Hunan, Peoples R China

来源：

ADVANCES IN APPLIED MATHEMATICS AND MECHANICS | 2017年 / 9卷 / 06期

基金：

中国国家自然科学基金; 国家高技术研究发展计划(863计划);

关键词：

Richardson extrapolation; Cascadicmultigrid; gradedmesh; elliptic problems; corner singularity; FINITE-ELEMENT-METHOD; CORNER SINGULARITIES; POISSON EQUATION; PARABOLIC PROBLEMS; COMPACT SCHEME; CONVERGENCE; COMPUTATION; REFINEMENTS; ALGORITHM; EXCMG;

D O I：

10.4208/aamm.OA-2016-0019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper proposes an extrapolation cascadic multigrid (EXCMG) method to solve elliptic problems in domains with reentrant corners. On a class of lambda-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.

引用

页码：1347 / 1363

页数：17

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