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Author:

Xu, Fei (Xu, Fei.) | Xie, Hehu (Xie, Hehu.) | Zhang, Ning (Zhang, Ning.)

Indexed by:

EI Scopus SCIE

Abstract:

A type of parallel augmented subspace scheme for eigenvalue problems is proposed by using coarse space in the multigrid method. With the help of coarse space in the multigrid method, solving the eigenvalue problem in the finest space is decomposed into solving the standard linear boundary value problems and very-low-dimensional eigenvalue problems. The computational efficiency can be improved since there is no direct eigenvalue solving in the finest space and the multigrid method can act as the solver for the deduced linear boundary value problems. Furthermore, for different eigenvalues, the corresponding boundary value problem and low-dimensional eigenvalue problem can be solved in the parallel way since they are independent of each other and there exists no data exchanging. This property means that we do not need to do the orthogonalization in the highest-dimensional spaces. This is the main aim of this paper since avoiding orthogonalization can improve the scalability of the proposed numerical method. Some numerical examples are provided to validate the proposed parallel augmented subspace method.

Keyword:

parallel augmented subspace method multigrid method parallel computing eigenvalue problems

Author Community:

  • [ 1 ] [Xu, Fei]Beijing Univ Technol, Fac Sci, Beijing Inst Sci & Engn Comp, Beijing 100124, Peoples R China
  • [ 2 ] [Xie, Hehu]Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC,NCMIS, Beijing 100190, Peoples R China
  • [ 3 ] [Xie, Hehu]Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
  • [ 4 ] [Zhang, Ning]Chinese Acad Sci, Inst Elect Engn, Beijing 100190, Peoples R China

Reprint Author's Address:

  • [Xu, Fei]Beijing Univ Technol, Fac Sci, Beijing Inst Sci & Engn Comp, Beijing 100124, Peoples R China

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Source :

SIAM JOURNAL ON SCIENTIFIC COMPUTING

ISSN: 1064-8275

Year: 2020

Issue: 5

Volume: 42

Page: A2655-A2677

3 . 1 0 0

JCR@2022

ESI Discipline: MATHEMATICS;

ESI HC Threshold:46

Cited Count:

WoS CC Cited Count: 2

SCOPUS Cited Count:

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 1

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