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Volumn 44, Issue 1, 2004, Pages 151-163

A black-box multigrid preconditioner for the biharmonic equation

Author keywords

Biharmonic equation; Finite elements; Mixed methods; Multigrid; Preconditioning

Indexed keywords


EID: 4043060898     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:BITN.0000025094.68655.c7     Document Type: Article
Times cited : (16)

References (17)
  • 1
    • 21744435054 scopus 로고    scopus 로고
    • Preconditioning discrete approximations of the Reissner-Mindlin plate model
    • D. N. Arnold, R. S. Falk, and R. Winther, Preconditioning discrete approximations of the Reissner-Mindlin plate model, Math. Modelling Numer. Anal., 31 (1997), pp. 517-557.
    • (1997) Math. Modelling Numer. Anal. , vol.31 , pp. 517-557
    • Arnold, D.N.1    Falk, R.S.2    Winther, R.3
  • 2
    • 84966241455 scopus 로고
    • Analysis of mixed methods using mesh dependent norms
    • I. Babuška, J. Osborn, and J. Pitkäranta, Analysis of mixed methods using mesh dependent norms, Math. Comput., 35 (1980), pp. 1039-1062.
    • (1980) Math. Comput. , vol.35 , pp. 1039-1062
    • Babuška, I.1    Osborn, J.2    Pitkäranta, J.3
  • 3
    • 0346796172 scopus 로고    scopus 로고
    • Block preconditioners for KKT systems in PDE-governed optimal control problems
    • R. H. W. Hoppe, K.-H. Hoffmann, and V. Schulz, eds., Birkhäuser, Berlin
    • A. Battermann and E. W. Sachs, Block preconditioners for KKT systems in PDE-governed optimal control problems, in Proceedings of Workshop on Fast Solutions of Discretised Optimisation Problems, R. H. W. Hoppe, K.-H. Hoffmann, and V. Schulz, eds., Birkhäuser, Berlin, 2001, pp. 1-18.
    • (2001) Proceedings of Workshop on Fast Solutions of Discretised Optimisation Problems , pp. 1-18
    • Battermann, A.1    Sachs, E.W.2
  • 4
    • 0004856636 scopus 로고
    • On the numerical solution of the biharmonic equation and the role of squaring matrices for preconditioning
    • D. Braess and P. Peisker, On the numerical solution of the biharmonic equation and the role of squaring matrices for preconditioning, IMA J. Numer. Anal., 6 (1986), pp. 393-404.
    • (1986) IMA J. Numer. Anal. , vol.6 , pp. 393-404
    • Braess, D.1    Peisker, P.2
  • 6
    • 0031082716 scopus 로고    scopus 로고
    • Efficient algorithms for solving a fourth order equation with the spectral Galerkin method
    • P. E. Bjørstad and B. P. Tjøstheim, Efficient algorithms for solving a fourth order equation with the spectral Galerkin method, SIAM J. Sci. Comput., 18 (1997), pp. 621-632.
    • (1997) SIAM J. Sci. Comput. , vol.18 , pp. 621-632
    • Bjørstad, P.E.1    Tjøstheim, B.P.2
  • 7
    • 0000382130 scopus 로고    scopus 로고
    • Minimum residual methods for augmented systems
    • B. Fischer, A. Ramage, D. Silvester, and A. J. Wathen, Minimum residual methods for augmented systems, BIT, 38 (1998), pp. 527-543.
    • (1998) BIT , vol.38 , pp. 527-543
    • Fischer, B.1    Ramage, A.2    Silvester, D.3    Wathen, A.J.4
  • 8
    • 0001604991 scopus 로고
    • Numerical methods for the first biharmonic equation and for the two-dimensional Stokes problem
    • R. Glowinski and O. Pironneau, Numerical methods for the first biharmonic equation and for the two-dimensional Stokes problem, SIAM Rev., 21 (1979), pp. 167-212.
    • (1979) SIAM Rev. , vol.21 , pp. 167-212
    • Glowinski, R.1    Pironneau, O.2
  • 9
    • 0027543238 scopus 로고
    • Multigrid preconditioning for the biharmonic Dirichlet problem
    • M. R. Hanisch, Multigrid preconditioning for the biharmonic Dirichlet problem, SIAM J. Numer. Anal., 30 (1993), pp. 184-214.
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 184-214
    • Hanisch, M.R.1
  • 10
    • 0034145598 scopus 로고    scopus 로고
    • Constraint preconditioning for indefinite linear systems
    • C. Keller, N. I. M. Gould, and A. J. Wathen, Constraint preconditioning for indefinite linear systems, SIAM J. Matrix Anal. Appl., 21 (2000), 1300-1317.
    • (2000) SIAM J. Matrix Anal. Appl. , vol.21 , pp. 1300-1317
    • Keller, C.1    Gould, N.I.M.2    Wathen, A.J.3
  • 12
    • 0004832943 scopus 로고
    • A multilevel algorithm for the biharmonic problem
    • P. Peisker, A multilevel algorithm for the biharmonic problem, Numer. Math., 46 (1985), pp. 623-634.
    • (1985) Numer. Math. , vol.46 , pp. 623-634
    • Peisker, P.1
  • 13
    • 0000971621 scopus 로고
    • A conjugate gradient method and a multigrid algorithm for Morley's finite element approximation of the biharmonic equation
    • P. Peisker and D. Braess, A conjugate gradient method and a multigrid algorithm for Morley's finite element approximation of the biharmonic equation, Numer. Math., 50 (1987), pp. 567-586.
    • (1987) Numer. Math. , vol.50 , pp. 567-586
    • Peisker, P.1    Braess, D.2
  • 14
    • 0034368563 scopus 로고    scopus 로고
    • Block-diagonal and indefinite symmetric preconditioners for mixed finite element formulations
    • I. Perugia and V. Simoncini, Block-diagonal and indefinite symmetric preconditioners for mixed finite element formulations, Numer. Linear Algebra Appl., 7 (2000), pp. 585-616.
    • (2000) Numer. Linear Algebra Appl. , vol.7 , pp. 585-616
    • Perugia, I.1    Simoncini, V.2
  • 15
    • 0001464667 scopus 로고
    • A preconditioned iterative method for saddle point problems
    • T. Rusten and R. Winther, A preconditioned iterative method for saddle point problems, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 887-904.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 887-904
    • Rusten, T.1    Winther, R.2
  • 16
    • 0028517184 scopus 로고
    • Fast iterative solution of stabilized Stokes systems. Part II: Using block preconditioners
    • D. Silvester and A. Wathen, Fast iterative solution of stabilized Stokes systems. Part II: Using block preconditioners, SIAM J. Numer. Anal., 31 (1994), pp. 1352-1367.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 1352-1367
    • Silvester, D.1    Wathen, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.