메뉴 건너뛰기




Volumn 33, Issue 2, 1996, Pages 555-570

Two-level Schwarz methods for the biharmonic problem discretized by conforming C1 elements

Author keywords

Biharmonic problem; Domain decomposition; Finite elements; Schwarz methods

Indexed keywords


EID: 0039053077     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/0733029     Document Type: Article
Times cited : (26)

References (35)
  • 1
    • 84966225192 scopus 로고
    • Convergence estimates for product iterative methods with applications to domain decomposition
    • J. H. BRAMBLE, J. E. PASCIAK, J. WANG, AND J. XU, Convergence estimates for product iterative methods with applications to domain decomposition, Math. Comp., 57 (1991), pp. 1-21.
    • (1991) Math. Comp. , vol.57 , pp. 1-21
    • Bramble, J.H.1    Pasciak, J.E.2    Wang, J.3    Xu, J.4
  • 2
    • 84966234195 scopus 로고
    • Parallel multilevel preconditioners
    • J. H. BRAMBLE, J. E. PASCIAK, AND J. XU, Parallel multilevel preconditioners, Math. Comp., 55 (1990), pp. 1-22.
    • (1990) Math. Comp. , vol.55 , pp. 1-22
    • Bramble, J.H.1    Pasciak, J.E.2    Xu, J.3
  • 3
    • 1542745731 scopus 로고    scopus 로고
    • Two-level additive Schwarz preconditioners for nonconforming finite element methods
    • to appear
    • S. C. BRENNER, Two-level additive Schwarz preconditioners for nonconforming finite element methods, Math. Comp., to appear.
    • Math. Comp.
    • Brenner, S.C.1
  • 6
    • 0001743874 scopus 로고
    • Domain decomposition algorithms for indefinite elliptic problems
    • X.-C. CAI AND O. WIDLUND, Domain decomposition algorithms for indefinite elliptic problems, SIAM J. Sci. Stat. Comput., 13 (1992), pp. 243-258.
    • (1992) SIAM J. Sci. Stat. Comput. , vol.13 , pp. 243-258
    • Cai, X.-C.1    Widlund, O.2
  • 7
    • 0027640852 scopus 로고
    • Multiplicative Schwarz algorithms for some nonsymmetric and indefinite problems
    • _, Multiplicative Schwarz algorithms for some nonsymmetric and indefinite problems, SIAM J. Numer. Anal., 30 (1993), pp. 936-952.
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 936-952
  • 9
    • 1542640446 scopus 로고
    • Domain Decomposition and Multigrid Methods for Elliptic Problems on Unstructured Meshes
    • Department of Mathematics, University of California at Los Angeles
    • T. F. CHAN AND B. F. SMITH, Domain Decomposition and Multigrid Methods for Elliptic Problems on Unstructured Meshes, CAM Report 93-42, Department of Mathematics, University of California at Los Angeles, 1993.
    • (1993) CAM Report 93-42
    • Chan, T.F.1    Smith, B.F.2
  • 10
    • 1542745725 scopus 로고
    • Additive Schwarz Domain Decomposition Methods for Elliptic Problems on Unstructured Meshes
    • Department of Mathematics, University of California at Los Angeles
    • T. F. CHAN AND J. ZOU, Additive Schwarz Domain Decomposition Methods for Elliptic Problems on Unstructured Meshes, CAM Report 93-40, Department of Mathematics, University of California at Los Angeles, 1993.
    • (1993) CAM Report 93-40
    • Chan, T.F.1    Zou, J.2
  • 12
    • 0028753150 scopus 로고
    • Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions
    • M. DRYJA, B. F. SMITH, AND O. B. WIDLUND, Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions, SIAM J. Numer. Anal., 31 (1994), pp. 1662-1694.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 1662-1694
    • Dryja, M.1    Smith, B.F.2    Widlund, O.B.3
  • 14
    • 0006182474 scopus 로고
    • Some domain decomposition algorithms for elliptic problems
    • L. Hayes and D. Kincaid, eds., Academic Press, San Diego, CA
    • _, Some domain decomposition algorithms for elliptic problems, in Iterative Methods for Large Linear Systems, L. Hayes and D. Kincaid, eds., Academic Press, San Diego, CA, 1989, pp. 273-291.
    • (1989) Iterative Methods for Large Linear Systems , pp. 273-291
  • 15
    • 1542535569 scopus 로고
    • Towards a unified theory of domain decomposition algorithms for elliptic problems
    • T. Chan, R. Glowinski, J. Périaux, and O. Widlund, eds., Society for Industrial and Applied Mathematics, Philadelphia, PA
    • _, Towards a unified theory of domain decomposition algorithms for elliptic problems, in Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, T. Chan, R. Glowinski, J. Périaux, and O. Widlund, eds., Society for Industrial and Applied Mathematics, Philadelphia, PA, 1990.
    • (1990) Third International Symposium on Domain Decomposition Methods for Partial Differential Equations
  • 16
    • 84990712164 scopus 로고
    • Schwarz methods of Neumann-Neumann type for three-dimensional elliptic finite element problems
    • _, Schwarz methods of Neumann-Neumann type for three-dimensional elliptic finite element problems, Comm. Pure Appl. Math., 48 (1995), pp. 121-155.
    • (1995) Comm. Pure Appl. Math. , vol.48 , pp. 121-155
  • 17
    • 0001159513 scopus 로고
    • Domain decomposition algorithms with small overlap
    • _, Domain decomposition algorithms with small overlap, SIAM J. Sci. Comput., 15 (1994), pp. 604-620.
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 604-620
  • 20
    • 34250079632 scopus 로고
    • Schwarz alternating and iterative refinement methods for mixed formulations of elliptic problems, part I: Algorithms and numerical results
    • T. P. MATHEW, Schwarz alternating and iterative refinement methods for mixed formulations of elliptic problems, part I: Algorithms and numerical results, Numer. Math., 65 (1993), pp. 445-468.
    • (1993) Numer. Math. , vol.65 , pp. 445-468
    • Mathew, T.P.1
  • 21
    • 21144467973 scopus 로고
    • Schwarz alternating and iterative refinement methods for mixed formulations of elliptic problems, part II: Theory
    • _, Schwarz alternating and iterative refinement methods for mixed formulations of elliptic problems, part II: Theory, Numer. Math., 65 (1993), pp. 469-492.
    • (1993) Numer. Math. , vol.65 , pp. 469-492
  • 26
    • 21344476056 scopus 로고
    • An additive Schwarz method for the p-version finite element method
    • _, An additive Schwarz method for the p-version finite element method, Numer. Math., 66 (1994), pp. 493-515.
    • (1994) Numer. Math. , vol.66 , pp. 493-515
  • 27
    • 0007414360 scopus 로고
    • Two-level Schwarz methods for nonconforming finite elements and discontinuous coefficients
    • N. D. Melson, T. A. Manteuffel, and S. F. McCormick, eds., NASA, Hampton, VA
    • M. SARKIS, Two-level Schwarz methods for nonconforming finite elements and discontinuous coefficients, in Proceedings of the Sixth Copper Mountain Conference on Multigrid Methods, Vol. 2, N. D. Melson, T. A. Manteuffel, and S. F. McCormick, eds., NASA, Hampton, VA, 1993, pp. 543-566.
    • (1993) Proceedings of the Sixth Copper Mountain Conference on Multigrid Methods , vol.2 , pp. 543-566
    • Sarkis, M.1
  • 29
    • 0000453571 scopus 로고
    • An optimal domain decomposition preconditioner for the finite element solution of linear elasticity problems
    • _, An optimal domain decomposition preconditioner for the finite element solution of linear elasticity problems, SIAM J. Sci. Stat. Comput., 13 (1992), pp. 364-378.
    • (1992) SIAM J. Sci. Stat. Comput. , vol.13 , pp. 364-378
  • 30
    • 0026995615 scopus 로고
    • Some Schwarz methods for symmetric and nonsymmetric elliptic problems
    • T. F. Chan, D. E. Keyes, G. A. Meurant, J. S. Scroggs, and R. G. Voigt, eds., Society for Industrial and Applied Mathematics, Philadelphia, PA
    • O. B. WIDLUND, Some Schwarz methods for symmetric and nonsymmetric elliptic problems, in Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, T. F. Chan, D. E. Keyes, G. A. Meurant, J. S. Scroggs, and R. G. Voigt, eds., Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992.
    • (1992) Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations
    • Widlund, O.B.1
  • 31
    • 0000570696 scopus 로고
    • Iterative methods by space decomposition and subspace correction
    • J. XU, Iterative methods by space decomposition and subspace correction, SIAM Rev., 34 (1992), pp. 581-613.
    • (1992) SIAM Rev. , vol.34 , pp. 581-613
    • Xu, J.1
  • 33
    • 0026966655 scopus 로고
    • Domain decomposition algorithms for the biharmonic Dirichlet problem
    • T. F. Chan, D. E. Keyes, G. A. Meurant, J. S. Scroggs, and R. G. Voigt, eds., Society for Industrial and Applied Mathematics, Philadelphia, PA
    • _, Domain decomposition algorithms for the biharmonic Dirichlet problem, in Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, T. F. Chan, D. E. Keyes, G. A. Meurant, J. S. Scroggs, and R. G. Voigt, eds., Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992.
    • (1992) Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations
  • 34
    • 34249840453 scopus 로고
    • Multilevel Schwarz methods
    • _, Multilevel Schwarz methods, Numer. Math., 63 (1992), pp. 521-539.
    • (1992) Numer. Math. , vol.63 , pp. 521-539
  • 35
    • 0001539061 scopus 로고
    • Multilevel Schwarz methods for the biharmonic Dirichlet problem
    • _, Multilevel Schwarz methods for the biharmonic Dirichlet problem, SIAM J. Sci. Comput., 15 (1994), pp. 621-644.
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 621-644


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.