메뉴 건너뛰기




Volumn 44, Issue 6, 1999, Pages 801-818

On a robust and scalable linear elasticity solver based on a saddle point formulation

Author keywords

Linear elasticity; Mixed finite elements; Multilevel iterative methods; Optimal order preconditioning; Parameter free solvers; Regularized Stokes equations

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; ITERATIVE METHODS; PROBLEM SOLVING;

EID: 0033079214     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19990228)44:6<801::AID-NME525>3.0.CO;2-Y     Document Type: Article
Times cited : (10)

References (24)
  • 3
    • 0029426091 scopus 로고
    • Scalable algorithms for the solution of Navier's equations of elasticity
    • O. Axelsson and M. Neytcheva, 'Scalable algorithms for the solution of Navier's equations of elasticity', J. Comput. Appl. Math., 63, 149-178 (1995).
    • (1995) J. Comput. Appl. Math. , vol.63 , pp. 149-178
    • Axelsson, O.1    Neytcheva, M.2
  • 4
    • 0039810560 scopus 로고    scopus 로고
    • On the additive version of the algebraic multilevel iteration method for anisotropic elliptic problems
    • University of Nijmegen, submitted
    • O. Axelsson and A. Padiy, 'On the additive version of the algebraic multilevel iteration method for anisotropic elliptic problems', Technical Report No 9711, University of Nijmegen, submitted.
    • Technical Report , vol.9711
    • Axelsson, O.1    Padiy, A.2
  • 9
    • 0024734081 scopus 로고
    • Error estimates and convergence rates for various incompressible elements
    • O. Zienkiewicz, Y. Liu and G. Huang, 'Error estimates and convergence rates for various incompressible elements', Int. J. Numer. Meth. Engng., 28, 2191-2202 (1989).
    • (1989) Int. J. Numer. Meth. Engng. , vol.28 , pp. 2191-2202
    • Zienkiewicz, O.1    Liu, Y.2    Huang, G.3
  • 11
    • 0017009452 scopus 로고
    • A class of iterative methods for finite element equations
    • O. Axelsson, 'A class of iterative methods for finite element equations', Comput. Meth. Appl. Mech. Engng., 9, 123-137 (1976).
    • (1976) Comput. Meth. Appl. Mech. Engng. , vol.9 , pp. 123-137
    • Axelsson, O.1
  • 12
    • 0001160426 scopus 로고
    • A generalized SSOR method
    • O. Axelsson, 'A generalized SSOR method', BIT, 12, 443-467 (1972).
    • (1972) BIT , vol.12 , pp. 443-467
    • Axelsson, O.1
  • 13
    • 0016555955 scopus 로고
    • Solutions of sparse linear systems of linear equations
    • C. Paige and M. Saunders, 'Solutions of sparse linear systems of linear equations', SIAM J. Numer. Anal., 12, 617-629 (1975).
    • (1975) SIAM J. Numer. Anal. , vol.12 , pp. 617-629
    • Paige, C.1    Saunders, M.2
  • 14
    • 0022739412 scopus 로고
    • On the convergence factor of Uzawa's algorithm
    • U. Langer and W. Queck, 'On the convergence factor of Uzawa's algorithm', J. Comput. Appl. Math., 15, 191-202 (1986).
    • (1986) J. Comput. Appl. Math. , vol.15 , pp. 191-202
    • Langer, U.1    Queck, W.2
  • 15
    • 0021211404 scopus 로고
    • A combined conjugate gradient-multigrid algorithm for the numerical solution of the Stokes problem
    • R. Verfürth, 'A combined conjugate gradient-multigrid algorithm for the numerical solution of the Stokes problem', IMA J. Numer. Anal., 4, 441-455 (1984).
    • (1984) IMA J. Numer. Anal. , vol.4 , pp. 441-455
    • Verfürth, R.1
  • 17
    • 0001619671 scopus 로고
    • Locking effects in the finite approximation of elasticity problems
    • I. Babuška and M. Suri, 'Locking effects in the finite approximation of elasticity problems', Numer. Math., 62, 439-463 (1992).
    • (1992) Numer. Math. , vol.62 , pp. 439-463
    • Babuška, I.1    Suri, M.2
  • 18
    • 0040997235 scopus 로고
    • Preconditioning of indefinite problems by regularization
    • O. Axelsson, 'Preconditioning of indefinite problems by regularization', SIAM J. Numer. Anal., 16, 58-69 (1979).
    • (1979) SIAM J. Numer. Anal. , vol.16 , pp. 58-69
    • Axelsson, O.1
  • 20
    • 0001341650 scopus 로고    scopus 로고
    • Analysis of the inexact Uzawa algorithm for saddle point problems
    • J. Bramble, J. Pasciak and A. Vassilev, 'Analysis of the inexact Uzawa algorithm for saddle point problems', SIAM J. Numer. Anal., 34, 1072-1092 (1997).
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 1072-1092
    • Bramble, J.1    Pasciak, J.2    Vassilev, A.3
  • 21
    • 85034127534 scopus 로고    scopus 로고
    • Block-triangular preconditioners for saddle point problems with a penalty term
    • to appear
    • A. Klawonn, 'Block-triangular preconditioners for saddle point problems with a penalty term', SIAM J. Sci. Comput., to appear.
    • SIAM J. Sci. Comput.
    • Klawonn, A.1
  • 22
    • 84966214346 scopus 로고
    • A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems
    • J. Bramble and J. Pasciak, 'A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems', Math. Comput., 50, 1-17 (1988).
    • (1988) Math. Comput. , vol.50 , pp. 1-17
    • Bramble, J.1    Pasciak, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.