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Volume 9, Issue 6
An Extrapolation Cascadic Multigrid Method for Elliptic Problems on Reentrant Domains

Kejia Pan, Dongdong He & Chuanmiao Chen

Adv. Appl. Math. Mech., 9 (2017), pp. 1347-1363.

Published online: 2017-09

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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.

  • AMS Subject Headings

65N55, 65N30

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COPYRIGHT: © Global Science Press

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@Article{AAMM-9-1347, author = {Pan , KejiaHe , Dongdong and Chen , Chuanmiao}, title = {An Extrapolation Cascadic Multigrid Method for Elliptic Problems on Reentrant Domains }, journal = {Advances in Applied Mathematics and Mechanics}, year = {2017}, volume = {9}, number = {6}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2016-0019}, url = {http://global-sci.org/intro/article_detail/aamm/10182.html} }
TY - JOUR T1 - An Extrapolation Cascadic Multigrid Method for Elliptic Problems on Reentrant Domains AU - Pan , Kejia AU - He , Dongdong AU - Chen , Chuanmiao JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1347 EP - 1363 PY - 2017 DA - 2017/09 SN - 9 DO - http://doi.org/10.4208/aamm.OA-2016-0019 UR - https://global-sci.org/intro/article_detail/aamm/10182.html KW - Richardson extrapolation, Cascadic multigrid, graded mesh, elliptic problems, corner singularity. AB -

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.

Kejia Pan, Dongdong He & Chuanmiao Chen. (2020). An Extrapolation Cascadic Multigrid Method for Elliptic Problems on Reentrant Domains . Advances in Applied Mathematics and Mechanics. 9 (6). 1347-1363. doi:10.4208/aamm.OA-2016-0019
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