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Volumn 93, Issue 3, 2003, Pages 445-470

Lower bounds for three-dimensional nonoverlapping domain decomposition algorithms

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EID: 0242641440     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110100376     Document Type: Article
Times cited : (7)

References (33)
  • 1
    • 0008765509 scopus 로고
    • On the spectra of sums of orthogonal projections with applications to parallel computing
    • P. Bjørstad, J. Mandel: On the spectra of sums of orthogonal projections with applications to parallel computing. BIT 31, 76-88 (1991)
    • (1991) BIT , vol.31 , pp. 76-88
    • Bjørstad, P.1    Mandel, J.2
  • 2
    • 0022918065 scopus 로고
    • Iterative methods for the solution of elliptic problems on regions partitioned into substructures
    • P.E. Bjørstad, O.B. Widlund: Iterative methods for the solution of elliptic problems on regions partitioned into substructures. SIAM J. Numer. Anal. 23, 1097-1120 (1986)
    • (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. I
    • J.H. Bramble, J.E. Pasciak, A.H. Schatz: The construction of preconditioners for elliptic problems by substructuring, I. Math. Comp. 47, 103-134 (1986)
    • (1986) Math. Comp. , vol.47 , pp. 103-134
    • Bramble, J.H.1    Pasciak, J.E.2    Schatz, A.H.3
  • 4
    • 84968495074 scopus 로고
    • The construction of preconditioners for elliptic problems by substructuring. IV
    • J.H. Bramble, J.E. Pasciak, A.M. Schatz: The construction of preconditioners for elliptic problems by substructuring. IV. Math. Comp. 53, 1-24 (1989)
    • (1989) Math. Comp. , vol.53 , pp. 1-24
    • Bramble, J.H.1    Pasciak, J.E.2    Schatz, A.M.3
  • 6
    • 0033415693 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, 25-52 (1999)
    • (1999) Numer. Math. , vol.83 , pp. 25-52
    • Brenner, S.C.1
  • 7
    • 0033709366 scopus 로고    scopus 로고
    • Lower bounds for two-level additive Schwarz preconditioners with small overlap
    • S.C. Brenner: Lower bounds for two-level additive Schwarz preconditioners with small overlap. SIAM J. Sci. Comp. 21, 1657-1669 (2000)
    • (2000) SIAM J. Sci. Comp. , vol.21 , pp. 1657-1669
    • Brenner, S.C.1
  • 9
    • 0011976893 scopus 로고    scopus 로고
    • Lower bounds for two-level additive Schwarz preconditioners for nonconforming finite elements
    • Advances in Computational Mathematics, Proceedings of the Guangzhou International Symposium, Z. Chen, Y. Li, C.A. Micchelli, Y. Xu, eds., Marcel Dekker, New York
    • S.C. Brenner, L.-Y. Sung: Lower bounds for two-level additive Schwarz preconditioners for nonconforming finite elements. Advances in Computational Mathematics, Proceedings of the Guangzhou International Symposium, Lecture Notes in Pure and Appl. Math. 202 (Z. Chen, Y. Li, C.A. Micchelli, Y. Xu, eds.), Marcel Dekker, New York, 1999, pp. 585-604
    • (1999) Lecture Notes in Pure and Appl. Math. , vol.202 , pp. 585-604
    • Brenner, S.C.1    Sung, L.-Y.2
  • 10
    • 0040792410 scopus 로고    scopus 로고
    • Lower bounds for nonoverlapping domain decomposition preconditioners in two dimensions
    • S.C. Brenner, L.-Y. Sung: Lower bounds for nonoverlapping domain decomposition preconditioners in two dimensions. Math. Comp. 69, 1319-1339 (2000)
    • (2000) Math. Comp. , vol.69 , pp. 1319-1339
    • Brenner, S.C.1    Sung, L.-Y.2
  • 11
    • 84974325009 scopus 로고
    • Domain decomposition algorithms
    • T.F. Chan, T.P. Mathew: Domain decomposition algorithms. Ada Numerica, 1994, pp. 61-143
    • (1994) Acta Numerica , pp. 61-143
    • Chan, T.F.1    Mathew, T.P.2
  • 13
    • 0007444976 scopus 로고
    • A method of domain decomposition for three dimensional finite element elliptic problems
    • R. Glowinski, G.H. Golub, G.A. Meurant, J. Périaux, eds., SIAM, Philadelphia
    • M. Dryja: A method of domain decomposition for three dimensional finite element elliptic problems. First International Symposium on Domain Decomposition Methods for Partial Differential Equations (R. Glowinski, G.H. Golub, G.A. Meurant, J. Périaux, eds.), SIAM, Philadelphia, 1988, pp. 43-61
    • (1988) First International Symposium on Domain Decomposition Methods for Partial Differential Equations , pp. 43-61
    • Dryja, M.1
  • 14
    • 0028753150 scopus 로고
    • Schwarz analysis of iterative substructuring algorithms for elliptic problems in three-dimensions
    • M. Dryja, B. F. Smith, O.B. Widlund: Schwarz analysis of iterative substructuring algorithms for elliptic problems in three-dimensions. SIAM J. Numer. Anal. 31, 1662-1694 (1994)
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 1662-1694
    • Dryja, M.1    Smith, B.F.2    Widlund, O.B.3
  • 15
    • 0006182474 scopus 로고
    • Some domain decomposition algorithms for elliptic problems
    • L. Hayes, D. Kincaid, eds., Academic Press, New York
    • M. Dryja, O.B. Widlund: Some domain decomposition algorithms for elliptic problems. Iterative Methods for Large Linear Systems (L. Hayes, 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
  • 16
    • 0002059273 scopus 로고
    • Towards a unified theory of domain decomposition algorithms for elliptic problems
    • T. Chan, R. Glowinski, J. Périaux, O.B. Widlund, eds., SIAM, Philadelphia
    • M. Dryja, O.B. Widlund: Towards a unified theory of domain decomposition algorithms for elliptic problems. Third International Symposium on Domain Decomposition Methods for Partial Differential Equations (T. Chan, R. Glowinski, J. Périaux, O.B. Widlund, eds.), SIAM, Philadelphia, 1990, pp. 3-21
    • (1990) Third International Symposium on Domain Decomposition Methods for Partial Differential Equations , pp. 3-21
    • Dryja, M.1    Widlund, O.B.2
  • 17
    • 0026978939 scopus 로고
    • Additive Schwarz methods for elliptic finite element problems in three dimensions
    • T.F. Chan, G.Meurant, J.S. Scroggs, R.G. Voigt, eds., SIAM, Philadelphia
    • M. Dryja, O.B. Widlund: Additive Schwarz methods for elliptic finite element problems in three dimensions. Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations (T.F. Chan, G.Meurant, J.S. Scroggs, R.G. Voigt, eds.), SIAM, Philadelphia, 1992, pp. 3-18
    • (1992) Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations , pp. 3-18
    • Dryja, M.1    Widlund, O.B.2
  • 18
    • 84990712164 scopus 로고
    • Schwarz methods of Neumann-Neumann type for three dimensional elliptic finite element problems
    • M. Dryja, O.B. Widlund: Schwarz methods of Neumann-Neumann type for three dimensional elliptic finite element problems. Comm. Pure Appl. Math. 48, 121-155 (1995)
    • (1995) Comm. Pure Appl. Math. , vol.48 , pp. 121-155
    • Dryja, M.1    Widlund, O.B.2
  • 19
    • 21844511143 scopus 로고
    • On the abstract theory of additive and multiplicative Schwarz algorithms
    • M. Griebel, P. Oswald: On the abstract theory of additive and multiplicative Schwarz algorithms. Numer. Math. 70, 163-180 (1995)
    • (1995) Numer. Math. , vol.70 , pp. 163-180
    • Griebel, M.1    Oswald, P.2
  • 21
    • 0028369940 scopus 로고
    • Domain decomposition methods in computational mechanics
    • P. Le Tallec: Domain decomposition methods in computational mechanics. Comput. Mech. Adv. 1, 121-220 (1994)
    • (1994) Comput. Mech. Adv. , vol.1 , pp. 121-220
    • Le Tallec, P.1
  • 23
    • 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, 1612-1620 (1990)
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 1612-1620
    • Mansfield, L.1
  • 31
    • 0026995615 scopus 로고
    • Some Schwarz methods for symmetric and nonsymmetric elliptic problems
    • D.E. Keyes, T.F. Chan, G. Meurant, J.S. Scroggs, R.G. Voigt, eds., SIAM, Philadelphia
    • O.B. Widlund: Some Schwarz methods for symmetric and nonsymmetric elliptic problems. Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, (D.E. Keyes, T.F. Chan, G. Meurant, J.S. Scroggs, R.G. Voigt, 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
  • 32
    • 0000570696 scopus 로고
    • Iterative methods by space decomposition and subspace correction
    • J. Xu: Iterative methods by space decomposition and subspace correction. SIAM Review 34, 581-613 (1992)
    • (1992) SIAM Review , vol.34 , pp. 581-613
    • Xu, J.1


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