An Improvement of Multigrid Methods Using Multiple Grids on Each Layer for Parallel Computing
Received:December 18, 2019  Revised:April 23, 2020
Key Words: linear systems   multigrid   preconditioner  
Fund Project: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).
Author NameAffiliation
Akira IMAKURA University of Tsukuba, $1$-$1$-$1$ Tennodai, Tsukuba, Ibaraki 305-8573, Japan 
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      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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