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An Extrapolation Cascadic Multigrid Method for Elliptic Problems on Reentrant Domains

Part of: Partial differential equations, boundary value problems

Published online by Cambridge University Press:  28 November 2017

Kejia Pan ,
Dongdong He  and
Chuanmiao Chen
Kejia Pan*
Affiliation:
School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, China
Dongdong He*
Affiliation:
School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
Chuanmiao Chen*
Affiliation:
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
*
*Corresponding author. Email:pankejia@hotmail.com (K. J. Pan), dongdonghe@tongji.edu.cn (D. D. He), cmchen@hunnu.edu.cn (C. M. Chen)
*Corresponding author. Email:pankejia@hotmail.com (K. J. Pan), dongdonghe@tongji.edu.cn (D. D. He), cmchen@hunnu.edu.cn (C. M. Chen)
*Corresponding author. Email:pankejia@hotmail.com (K. J. Pan), dongdonghe@tongji.edu.cn (D. D. He), cmchen@hunnu.edu.cn (C. M. Chen)
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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.

Keywords

Richardson extrapolationCascadic multigridgraded meshelliptic problemscorner singularity

MSC classification

Secondary: 65N55: Multigrid methods; domain decomposition 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 6 , December 2017 , pp. 1347 - 1363
Copyright
Copyright © Global-Science Press 2017 

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