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Volumn 20, Issue 5, 2013, Pages 832-851

Analysis of a two-level method for anisotropic diffusion equations on aligned and nonaligned grids

Author keywords

Anisotropic problem; Finite element discretization; Iterative methods; Two level methods

Indexed keywords


EID: 84883766349     PISSN: 10705325     EISSN: 10991506     Source Type: Journal    
DOI: 10.1002/nla.1847     Document Type: Article
Times cited : (6)

References (19)
  • 1
    • 0007452289 scopus 로고
    • New estimates of the contraction number of V-cycle multi-grid with applications to anisotropic equations
    • Notes on Numerical Fluid Mechanics. Vieweg: Braunschweig
    • Stevenson R. New estimates of the contraction number of V-cycle multi-grid with applications to anisotropic equations. In Incomplete Decomposition ( ILU)-Algorithms, Theory and Applications (Kiel, 1992), Vol.41, Notes on Numerical Fluid Mechanics. Vieweg: Braunschweig, 1993; 159-167.
    • (1993) Incomplete Decomposition ( ILU)-Algorithms, Theory and Applications (Kiel, 1992) , vol.41 , pp. 159-167
    • Stevenson, R.1
  • 2
    • 0007431321 scopus 로고
    • Robust multi-grid with 7-point ILU smoothing
    • In, International Series of Numerical Mathematics. Birkhäuser: Basel
    • Stevenson R. Robust multi-grid with 7-point ILU smoothing. In Multigrid Methods, IV (Amsterdam, 1993), Vol.116, International Series of Numerical Mathematics. Birkhäuser: Basel, 1994; 295-307.
    • (1994) Multigrid Methods, IV (Amsterdam, 1993) , vol.116 , pp. 295-307
    • Stevenson, R.1
  • 3
    • 0004279470 scopus 로고
    • Springer Series in Computational Mathematics, Springer-Verlag: Berlin
    • Hackbusch W. Multigrid methods and applications, Springer Series in Computational Mathematics, Vol.4. Springer-Verlag: Berlin, 1985.
    • (1985) Multigrid methods and applications , vol.4
    • Hackbusch, W.1
  • 4
    • 0035531364 scopus 로고    scopus 로고
    • Uniform convergence of the multigrid V-cycle for an anisotropic problem
    • Bramble JH, Zhang X. Uniform convergence of the multigrid V-cycle for an anisotropic problem. Mathematics of Computation 2001; 70(234):453-470.
    • (2001) Mathematics of Computation , vol.70 , Issue.234 , pp. 453-470
    • Bramble, J.H.1    Zhang, X.2
  • 5
    • 84966255975 scopus 로고
    • Convergence estimates for multigrid algorithms without regularity assumptions
    • Bramble JH, Pasciak JE, Wang JP, Xu J. Convergence estimates for multigrid algorithms without regularity assumptions. Mathematics of Computation 1991; 57(195):23-45.
    • (1991) Mathematics of Computation , vol.57 , Issue.195 , pp. 23-45
    • Bramble, J.H.1    Pasciak, J.E.2    Wang, J.P.3    Xu, J.4
  • 6
    • 0000570696 scopus 로고
    • Iterative methods by space decomposition and subspace correction
    • Xu J. Iterative methods by space decomposition and subspace correction. SIAM Review 1992; 34(4):581-613.
    • (1992) SIAM Review , vol.34 , Issue.4 , pp. 581-613
    • Xu, J.1
  • 7
    • 0000696868 scopus 로고    scopus 로고
    • V-cycle convergence with unsymmetric smoothers and application to an anisotropic model problem
    • (electronic)
    • Neuss N. V-cycle convergence with unsymmetric smoothers and application to an anisotropic model problem. SIAM Journal on Numerical Analysis 1998; 35(3):1201-1212 (electronic).
    • (1998) SIAM Journal on Numerical Analysis , vol.35 , Issue.3 , pp. 1201-1212
    • Neuss, N.1
  • 8
    • 84867507394 scopus 로고    scopus 로고
    • Convergence analysis of V-cycle multigrid method for anisotropic elliptic equation
    • DOI: 10.1093/imanum/drr043.
    • Wu Y, Chen L, Xie X, Xu J. Convergence analysis of V-cycle multigrid method for anisotropic elliptic equation. IMA Journal of Numerical Analysis 2012. DOI: 10.1093/imanum/drr043.
    • (2012) IMA Journal of Numerical Analysis
    • Wu, Y.1    Chen, L.2    Xie, X.3    Xu, J.4
  • 9
    • 0000277689 scopus 로고
    • Tensor product type subspace splittings and multilevel iterative methods for anisotropic problems
    • Griebel M, Oswald P. Tensor product type subspace splittings and multilevel iterative methods for anisotropic problems. Advances in Computational Mathematics 1995; 4(1-2):171-206.
    • (1995) Advances in Computational Mathematics , vol.4 , Issue.1-2 , pp. 171-206
    • Griebel, M.1    Oswald, P.2
  • 10
    • 0000779223 scopus 로고
    • Algebraic multilevel preconditioning methods. I
    • Axelsson O, Vassilevski PS. Algebraic multilevel preconditioning methods. I. Numerische Mathematik 1989; 56(2-3):157-177.
    • (1989) Numerische Mathematik , vol.56 , Issue.2-3 , pp. 157-177
    • Axelsson, O.1    Vassilevski, P.S.2
  • 14
    • 21244465514 scopus 로고    scopus 로고
    • On multilevel preconditioners which are optimal with respect to both problem and discretization parameters
    • Axelsson O, Margenov S. On multilevel preconditioners which are optimal with respect to both problem and discretization parameters. Computational Methods in Applied Mathematics 2003; 3(1):6-22.
    • (2003) Computational Methods in Applied Mathematics , vol.3 , Issue.1 , pp. 6-22
    • Axelsson, O.1    Margenov, S.2
  • 15
    • 22144472995 scopus 로고    scopus 로고
    • Robust optimal multilevel preconditioners for non-conforming finite element systems
    • Blaheta R, Margenov S, Neytcheva M. Robust optimal multilevel preconditioners for non-conforming finite element systems. Numerical Linear Algebra with Applications 2005; 12(5-6):495-514.
    • (2005) Numerical Linear Algebra with Applications , vol.12 , Issue.5-6 , pp. 495-514
    • Blaheta, R.1    Margenov, S.2    Neytcheva, M.3
  • 16
    • 51349137357 scopus 로고    scopus 로고
    • On the multilevel preconditioning of Crouzeix-Raviart elliptic problems
    • Kraus J, Margenov S, Synka J. On the multilevel preconditioning of Crouzeix-Raviart elliptic problems. Numerical Linear Algebra with Applications 2008; 15(5):395-416.
    • (2008) Numerical Linear Algebra with Applications , vol.15 , Issue.5 , pp. 395-416
    • Kraus, J.1    Margenov, S.2    Synka, J.3
  • 18
    • 51449106109 scopus 로고    scopus 로고
    • Two-sided bounds on the convergence rate of two-level methods
    • Zikatanov LT. Two-sided bounds on the convergence rate of two-level methods. Numerical Linear Algebra with Applications 2008; 15(5):439-454.
    • (2008) Numerical Linear Algebra with Applications , vol.15 , Issue.5 , pp. 439-454
    • Zikatanov, L.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.