| Akira IMAKURA.An Improvement of Multigrid Methods Using Multiple Grids on Each Layer for Parallel Computing[J].数学研究及应用,2021,41(1):87~98 |
| An Improvement of Multigrid Methods Using Multiple Grids on Each Layer for Parallel Computing |
| An Improvement of Multigrid Methods Using Multiple Grids on Each Layer for Parallel Computing |
| 投稿时间：2019-12-18 修订日期：2020-04-23 |
| DOI：10.3770/j.issn:2095-2651.2021.01.009 |
| 中文关键词: linear systems multigrid preconditioner |
| 英文关键词:linear systems multigrid preconditioner |
| 基金项目:Supported by the Japan Science and Technology Agency (JST), ACT-I (Grant No.JPMJPR16U6) and the Japan Society for the Promotion of Science (JSPS), Grants-in-Aid for Scientific Research (Grant Nos.17K12690; 18H03250; 19KK0255). |
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| 中文摘要: |
| Multigrid methods are widely used and well studied for linear solvers and preconditioners of Krylov subspace methods. The multigrid method is one of the most powerful approaches for solving large scale linear systems; however, it may show low parallel efficiency on coarse grids. There are several kinds of research on this issue. In this paper, we intend to overcome this difficulty by proposing a novel multigrid algorithm that has multiple grids on each layer. Numerical results indicate that the proposed method shows a better convergence rate compared with the existing multigrid method. |
| 英文摘要: |
| Multigrid methods are widely used and well studied for linear solvers and preconditioners of Krylov subspace methods. The multigrid method is one of the most powerful approaches for solving large scale linear systems; however, it may show low parallel efficiency on coarse grids. There are several kinds of research on this issue. In this paper, we intend to overcome this difficulty by proposing a novel multigrid algorithm that has multiple grids on each layer. Numerical results indicate that the proposed method shows a better convergence rate compared with the existing multigrid method. |
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