메뉴 건너뛰기




Volumn 21, Issue 5, 2000, Pages 1657-1669

Lower bounds for two-level additive schwarz preconditioners with small overlap

Author keywords

[No Author keywords available]

Indexed keywords

LINEAR EQUATIONS; MATHEMATICAL OPERATORS; PROBLEM SOLVING; VARIATIONAL TECHNIQUES;

EID: 0033709366     PISSN: 10648275     EISSN: None     Source Type: None    
DOI: 10.1137/S1064827598336483     Document Type: Article
Times cited : (23)

References (25)
  • 1
    • 0008765509 scopus 로고
    • On the spectra of sums of orthogonal projections with applications to parallel computing
    • P.E. BJØRSTAD AND J. MANDEL, On the spectra of sums of orthogonal projections with applications to parallel computing, BIT, 31 (1991), pp. 76-88.
    • (1991) BIT , vol.31 , pp. 76-88
    • BjØrstad, P.E.1    Mandel, J.2
  • 2
    • 0022918065 scopus 로고
    • Iterative methods for the solution of elliptic problems on regions partitioned into substructures
    • P.E. BJØRSTAD AND O.B. WIDLUND, Iterative methods for the solution of elliptic problems on regions partitioned into substructures, SIAM J. Numer. Anal., 23 (1986), pp. 1097-1120.
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 1097-1120
    • BjØrstad, P.E.1    Widlund, O.B.2
  • 3
    • 84966199070 scopus 로고
    • The construction of preconditioners for elliptic problems by substructuring
    • J.H. BRAMBLE, J.E. PASCIAK, AND A.H. SCHATZ, The construction of preconditioners for elliptic problems by substructuring, I, Math. Comp., 47 (1986), pp. 103-104.
    • (1986) I, Math. Comp. , vol.47 , pp. 103-104
    • Bramble, J.H.1    Pasciak, J.E.2    Schatz, A.H.3
  • 4
    • 0030526898 scopus 로고    scopus 로고
    • A two-level additive Schwarz preconditioner for nonconforming plate elements
    • S.C. BRENNER, A two-level additive Schwarz preconditioner for nonconforming plate elements, Numer. Math., 72 (1996), pp. 419-447.
    • (1996) Numer. Math. , vol.72 , pp. 419-447
    • Brenner, S.C.1
  • 5
    • 0043042946 scopus 로고
    • A two-level additive Schwarz preconditioner for macro-element approximations of the plate bending problem
    • S.C. BRENNER, A two-level additive Schwarz preconditioner for macro-element approximations of the plate bending problem, Houston J. Math., 21 (1995), pp. 823-844.
    • (1995) Houston J. Math. , vol.21 , pp. 823-844
    • Brenner, S.C.1
  • 6
    • 0033443378 scopus 로고    scopus 로고
    • The condition number of the Schur complement in domain decomposition
    • S.C. BRENNER, The condition number of the Schur complement in domain decomposition, Numer. Math., 83 (1999), pp. 187-203.
    • (1999) Numer. Math. , vol.83 , pp. 187-203
    • Brenner, S.C.1
  • 8
    • 0033415693 scopus 로고    scopus 로고
    • Balancing domain decomposition for nonconforming plate elements
    • S.C. BRENNER AND L.-Y. SUNG, Balancing domain decomposition for nonconforming plate elements, Numer. Math., 83 (1999), pp. 25-52.
    • (1999) Numer. Math. , vol.83 , pp. 25-52
    • Brenner, S.C.1    Sung, L.-Y.2
  • 9
    • 0011976893 scopus 로고    scopus 로고
    • Lower bounds for two-level additive schwarz preconditioners for nonconforming finite elements
    • Z. Chen, Y. Li, C.A. Micchelli, and Y. Xu, eds., Lecture Notes in Pure and Appl. Math., Marcel Dekker, New York
    • S.C. BRENNER AND L.-Y. SUNG, Lower bounds for two-level additive Schwarz preconditioners for nonconforming finite elements, in Advances in Computational Mathematics, Proceedings of the Guangzhou International Symposium, Z. Chen, Y. Li, C.A. Micchelli, and Y. Xu, eds., Lecture Notes in Pure and Appl. Math., 202, Marcel Dekker, New York, 1999, pp. 585-604.
    • (1999) Advances in Computational Mathematics, Proceedings of the Guangzhou International Symposium , vol.202 , pp. 585-604
    • Brenner, S.C.1    Sung, L.-Y.2
  • 10
    • 84974325009 scopus 로고
    • Domain decomposition algorithms
    • Cambridge University Press, Cambridge, UK
    • T.F. CHAN AND T.P. MATHEW, Domain decomposition algorithms, in Acta Numerica, Cambridge University Press, Cambridge, UK, 1994, pp. 61-143.
    • (1994) Acta Numerica , pp. 61-143
    • Chan, T.F.1    Mathew, T.P.2
  • 13
    • 0006182474 scopus 로고
    • Some domain decomposition algorithms for elliptic problems
    • L. Hayes and D. Kincaid, eds., Academic Press, New York
    • M. DRYJA AND O.B. WIDLUND, Some domain decomposition algorithms for elliptic problems, in Iterative Methods for Large Linear Systems, L. Hayes and D. Kincaid, eds., Academic Press, New York, 1989, pp. 273-291.
    • (1989) Iterative Methods for Large Linear Systems , pp. 273-291
    • Dryja, M.1    Widlund, O.B.2
  • 14
    • 0001159513 scopus 로고
    • Domain decomposition algorithms with small overlap
    • M. DRYJA AND O.B. WIDLUND, 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
    • Dryja, M.1    Widlund, O.B.2
  • 15
    • 21844511143 scopus 로고
    • On the abstract theory of additive and multiplicative Schwarz algorithms
    • M. GRIEBEL AND P. OSWALD, On the abstract theory of additive and multiplicative Schwarz algorithms, Numer. Math., 70 (1995), pp. 163-180.
    • (1995) Numer. Math. , vol.70 , pp. 163-180
    • Griebel, M.1    Oswald, P.2
  • 17
    • 0001115526 scopus 로고    scopus 로고
    • A Neumann-Neumann domain decomposition algorithm for solving plate and shell problems
    • P. LE TALLEC, J. MANDEL, AND M. VIDRASCU, A Neumann-Neumann domain decomposition algorithm for solving plate and shell problems, SIAM J. Numer. Anal., 35 (1998), pp. 836-867.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 836-867
    • Le Tallec, P.1    Mandel, J.2    Vidrascu, M.3
  • 19
    • 0000368999 scopus 로고
    • On the conjugate gradient solution of the Schur complement system obtained from domain decomposition
    • L. MANSFIELD, On the conjugate gradient solution of the Schur complement system obtained from domain decomposition, SIAM J. Numer. Anal., 27 (1990), pp. 1612-1620.
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 1612-1620
    • Mansfield, L.1
  • 23
    • 0000208364 scopus 로고
    • An extension theorem for finite element spaces with three applications
    • W. Hackbusch and K. Witsch, eds., Friedr. Vieweg und Sohn, Braunschweig/Wiesbaden
    • O.B. WIDLUND, An extension theorem for finite element spaces with three applications, in Numerical Techniques in Continuum Mechanics, W. Hackbusch and K. Witsch, eds., Friedr. Vieweg und Sohn, Braunschweig/Wiesbaden, 1987, pp. 110-122.
    • (1987) Numerical Techniques in Continuum Mechanics , pp. 110-122
    • Widlund, O.B.1
  • 24
    • 0026995615 scopus 로고
    • Some Schwarz methods for symmetric and nonsymmetric elliptic problems
    • D.E. Keyes, T.F. Chan, G. Meurant, J.S. Scroggs, and R.G. Voight, eds., SIAM, Philadelphia
    • O.B. WIDLUND, Some Schwarz methods for symmetric and nonsymmetric elliptic problems, in Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, D.E. Keyes, T.F. Chan, G. Meurant, J.S. Scroggs, and R.G. Voight, eds., SIAM, Philadelphia, 1991, pp. 19-36.
    • (1991) Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations , pp. 19-36
    • Widlund, O.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.