Year: 2017
Author: Kejia Pan, Dongdong He, Chuanmiao Chen
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 6 : pp. 1347–1363
Abstract
This paper proposes an extrapolation cascadic multigrid (EXCMG) method to solve elliptic problems in domains with reentrant corners. On a class of λ-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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2016-0019
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 6 : pp. 1347–1363
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Richardson extrapolation Cascadic multigrid graded mesh elliptic problems corner singularity.
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