| Economical cascadic multigrid method (ECMG) |
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| 引用本文： | Zhong-ci SHI~1 Xue-jun XU~(1 ) Yun-qing HUANG~2 ~1 LSEC,Institute of Computational Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100080,China,~2 Hunan Key Laboratory for Computation and Simulation in Science and Engineering,Institute for Computational and Applied Mathematics,Xiangtan University,Xiangtan 411105,China. Economical cascadic multigrid method (ECMG)[J]. 中国科学A辑(英文版), 2007, 50(12): 1765-1780. DOI: 10.1007/s11425-007-0127-z |
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| 作者姓名： | Zhong-ci SHI~1 Xue-jun XU~(1 ) Yun-qing HUANG~2 ~1 LSEC Institute of Computational Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China ~2 Hunan Key Laboratory for Computation and Simulation in Science and Engineering Institute for Computational and Applied Mathematics Xiangtan University Xiangtan 411105 China |
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| 作者单位： | Zhong-ci SHI（LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China） ;Xue-jun XU（LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China） ;Yun-qing HUANG（Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Institute for Computational and Applied Mathematics, Xiangtan University, Xiangtan 411105, China） ; |
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| 基金项目： | 国家自然科学基金;教育部高等学校博士学科点专项科研基金 |
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| 摘 要： | In this paper,an economical cascadic multigrid method is proposed.Compared with the usual cascadic multigrid method developed by Bornemann and Deuflhard,the new one requires less iterations on each level,especially on the coarser grids.Many operations can be saved in the new cascadic multigrid algorithms.The main ingredient is the control of the iteration numbers on the each level to preserve the accuracy without over iterations.The theoretical justification is based on the observations that the error reduction rate of an iteration scheme in terms of the smoothing property is no longer accurate while the iteration number is big enough.A new formulae of the error reduction rate is employed in our new algorithm.Numerical experiments are reported to support our theory.
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| 收稿时间： | 2007-04-09 |
| 修稿时间： | 2007-06-22 |
Economical cascadic multigrid method (ECMG) |
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| Zhong-ci Shi,Xue-jun Xu,Yun-qing Huang. Economical cascadic multigrid method (ECMG)[J]. Science in China(Mathematics), 2007, 50(12): 1765-1780. DOI: 10.1007/s11425-007-0127-z |
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| Authors: | Zhong-ci Shi Xue-jun Xu Yun-qing Huang |
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| Affiliation: | 1. LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China
2. Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Institute for Computational and Applied Mathematics, Xiangtan University, Xiangtan 411105, China |
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| Abstract: | In this paper,an economical cascadic multigrid method is proposed.Compared with the usual cascadic multigrid method developed by Bornemann and Deuflhard,the new one requires less iterations on each level,especially on the coarser grids.Many operations can be saved in the new cascadic multigrid algorithms.The main ingredient is the control of the iteration numbers on the each level to preserve the accuracy without over iterations.The theoretical justification is based on the observations that the error reduction rate of an iteration scheme in terms of the smoothing property is no longer accurate while the iteration number is big enough.A new formulae of the error reduction rate is employed in our new algorithm.Numerical experiments are reported to support our theory. |
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| Keywords: | economical cascadic multigrid method (ECMG) cascadic multigrid method (CMG) |
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