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Volumn 33, Issue 1-2, 1997, Pages 193-209

Iterative substructuring methods for spectral elements: Problems in three dimensions based on numerical quadrature

Author keywords

Domain decomposition; Gauss Lobatto Legendre quadrature; Iterative substructuring; Preconditioned conjugate gradient methods; Spectral finite element approximation

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; FUNCTIONS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; PARTIAL DIFFERENTIAL EQUATIONS; PIECEWISE LINEAR TECHNIQUES; PROBLEM SOLVING;

EID: 0030826037     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0898-1221(96)00230-1     Document Type: Article
Times cited : (13)

References (36)
  • 1
    • 0000094594 scopus 로고
    • An iterative method for the solution of the eigenvalue problem of linear differential and integral operators
    • C. Lanczos, An iterative method for the solution of the eigenvalue problem of linear differential and integral operators, J. Res. Nat. Bur. Standards Sect. B. 45, 225-280 (1950).
    • (1950) J. Res. Nat. Bur. Standards Sect. B. , vol.45 , pp. 225-280
    • Lanczos, C.1
  • 3
    • 85162699057 scopus 로고
    • Trigonometric interpolation of empirical and analytical functions
    • C. Lanczos, Trigonometric interpolation of empirical and analytical functions, J. Math. Phys. 17, 123-199 (1938).
    • (1938) J. Math. Phys. , vol.17 , pp. 123-199
    • Lanczos, C.1
  • 10
    • 0042969918 scopus 로고
    • Domain decomposition methods in science and engineering
    • Proceedings of the Seventh International Conference on Domain Decomposition, October 27-30, Pennsylvania State University, (Edited by D.E. Keyes and J. Xu), AMS, Providence, RI
    • Domain decomposition methods in science and engineering, In Proceedings of the Seventh International Conference on Domain Decomposition, October 27-30, 1993, Pennsylvania State University, Contemporary Mathematics, Volume 180, (Edited by D.E. Keyes and J. Xu), AMS, Providence, RI, (1994).
    • (1993) Contemporary Mathematics , vol.180
  • 11
    • 0028753150 scopus 로고
    • Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions
    • December
    • 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 (6), 1662-1694 (December 1994).
    • (1994) SIAM J. Numer. Anal. , vol.31 , Issue.6 , pp. 1662-1694
    • Dryja, M.1    Smith, B.F.2    Widlund, O.B.3
  • 12
    • 0039216197 scopus 로고
    • Exotic coarse spaces for Schwarz methods for lower order and spectral finite elements
    • Seventh International Conference of Domain Decomposition Methods in Scientific and Engineering Computing, October 27-30, Pennsylvania State University, (Edited by D.E. Keyes and J. Xu), AMS
    • O.B. Widlund, Exotic coarse spaces for Schwarz methods for lower order and spectral finite elements, In Seventh International Conference of Domain Decomposition Methods in Scientific and Engineering Computing, October 27-30, 1993, Pennsylvania State University, Contemporary Mathematics, Volume 180, (Edited by D.E. Keyes and J. Xu), pp. 131-136, AMS, (1994).
    • (1993) Contemporary Mathematics , vol.180 , pp. 131-136
    • Widlund, O.B.1
  • 13
    • 0030556926 scopus 로고    scopus 로고
    • Multilevel Schwarz methods for elliptic problems with discontinuous coefficients in three dimensions
    • M. Dryja, M.V. Sarkis, and O.B. Widlund, Multilevel Schwarz methods for elliptic problems with discontinuous coefficients in three dimensions, Numer. Math. 72 (3), 313-348 (1996).
    • (1996) Numer. Math. , vol.72 , Issue.3 , pp. 313-348
    • Dryja, M.1    Sarkis, M.V.2    Widlund, O.B.3
  • 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, 604-620 (1994).
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 604-620
    • Dryja, M.1    Widlund, O.B.2
  • 15
    • 0042969916 scopus 로고
    • Some recent results on Schwarz type domain decomposition algorithms
    • Como, Italy, June 15-19, (Edited by Y.A. Kuznetsov, J. Périaux, A. Quarteroni and O.B. Widlund), AMS
    • M. Dryja and O.B. Widlund, Some recent results on Schwarz type domain decomposition algorithms, Presented at the Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition, Como, Italy, June 15-19, 1992, Vol. 157, (Edited by Y.A. Kuznetsov, J. Périaux, A. Quarteroni and O.B. Widlund), AMS, (1994).
    • (1992) Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition , vol.157
    • Dryja, M.1    Widlund, O.B.2
  • 16
    • 84990712164 scopus 로고
    • Schwarz methods of Neumann-Neumann type for three-dimensional elliptic finite element problems
    • February
    • M. Dryja and O.B. Widlund, Schwarz methods of Neumann-Neumann type for three-dimensional elliptic finite element problems, Comm. Pure Appl. Math. 48 (2), 121-155 (February 1995).
    • (1995) Comm. Pure Appl. Math. , vol.48 , Issue.2 , pp. 121-155
    • Dryja, M.1    Widlund, O.B.2
  • 17
    • 0000337361 scopus 로고    scopus 로고
    • A polylogarithmic bound for an iterative substructuring method for spectral elements in three dimensions
    • August
    • L.F. Pavarino and O.B. Widlund, A polylogarithmic bound for an iterative substructuring method for spectral elements in three dimensions, SIAM J. Numer. Anal 33 (4), 1303-1335 (August 1996).
    • (1996) Siam J. Numer. Anal , vol.33 , Issue.4 , pp. 1303-1335
    • Pavarino, L.F.1    Widlund, O.B.2
  • 19
    • 0026963296 scopus 로고
    • Parallel computing and domain decomposition
    • Edited by T.F. Chan, D.E. Keyes, G.A. Meurant, J.S. Scroggs and R.G. Voigt, SIAM, Philadelphia, PA
    • W.D. Gropp, Parallel computing and domain decomposition, Presented at the Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, (Edited by T.F. Chan, D.E. Keyes, G.A. Meurant, J.S. Scroggs and R.G. Voigt), SIAM, Philadelphia, PA, (1992).
    • (1992) Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations
    • Gropp, W.D.1
  • 20
    • 0026976848 scopus 로고
    • A comparison of some domain decomposition algorithms for nonsymmetric elliptic problems
    • Edited by T.F. Chan, D.E. Keyes, G.A. Meurant, J.S. Scroggs and R.G. Voigt, SIAM, Philadelphia, PA
    • X.-C. Cai, W.D. Gropp and D.E. Keyes, A comparison of some domain decomposition algorithms for nonsymmetric elliptic problems, In Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, (Edited by T.F. Chan, D.E. Keyes, G.A. Meurant, J.S. Scroggs and R.G. Voigt), SIAM, Philadelphia, PA, (1992).
    • (1992) Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations
    • Cai, X.-C.1    Gropp, W.D.2    Keyes, D.E.3
  • 21
    • 84985341546 scopus 로고
    • A comparison of some domain decomposition and ILU preconditioned iterative methods for nonsymmetric elliptic problems
    • X.-C. Cai, W.D. Gropp and D.E. Keyes, A comparison of some domain decomposition and ILU preconditioned iterative methods for nonsymmetric elliptic problems, Numer. Lin. Alg. Appl. 1 (5), 477-504 (1994).
    • (1994) Numer. Lin. Alg. Appl. , vol.1 , Issue.5 , pp. 477-504
    • Cai, X.-C.1    Gropp, W.D.2    Keyes, D.E.3
  • 22
    • 21844508844 scopus 로고
    • Balancing domain decomposition for mixed finite elements
    • July
    • L.C. Cowsar, J. Mandel and M.F. Wheeler, Balancing domain decomposition for mixed finite elements, Math. Comp. 64 (211), 989-1015 (July 1995).
    • (1995) Math. Comp. , vol.64 , Issue.211 , pp. 989-1015
    • Cowsar, L.C.1    Mandel, J.2    Wheeler, M.F.3
  • 23
    • 0042468730 scopus 로고
    • Experiences with domain decomposition in three dimensions: Overlapping Schwarz methods
    • Como, Italy, June 15-19, (Edited by Y.A. Kuznetsov, J. Périaux, A. Quarteroni and O.B. Widlund), AMS
    • W.D. Gropp and B.F. Smith, Experiences with domain decomposition in three dimensions: Overlapping Schwarz methods, Presented at the Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition, Como, Italy, June 15-19, 1992, Vol. 157, (Edited by Y.A. Kuznetsov, J. Périaux, A. Quarteroni and O.B. Widlund), AMS, (1994).
    • (1992) Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition , vol.157
    • Gropp, W.D.1    Smith, B.F.2
  • 24
    • 0003559010 scopus 로고
    • A parallel implementation of an iterative substructuring algorithm for problems in three dimensions
    • B.F. Smith, A parallel implementation of an iterative substructuring algorithm for problems in three dimensions, SIAM J. Sci. Comput. 14, 406-423 (1993).
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 406-423
    • Smith, B.F.1
  • 25
    • 0041025990 scopus 로고
    • Iterative substructuring methods for spectral elements in three dimensions
    • (Edited by M. Křižek, P. Neittaanmäki and R. Stenberg) Marcel Dekker, New York
    • L.F. Pavarino and O.B. Widlund, Iterative substructuring methods for spectral elements in three dimensions, In The Finite Element Method: Fifty Years of the Courant Element, (Edited by M. Křižek, P. Neittaanmäki and R. Stenberg) pp. 345-355, Marcel Dekker, New York, (1994).
    • (1994) The Finite Element Method: Fifty Years of the Courant Element , pp. 345-355
    • Pavarino, L.F.1    Widlund, O.B.2
  • 26
    • 0041968154 scopus 로고
    • A wire basket based method for spectral elements in three dimensions
    • October 27-30, Pennsylvania State University, Contemporary Mathematics, (Edited by D.E. Keyes and J. Xu), pp. 99-104, AMS
    • L.F. Pavarino, A wire basket based method for spectral elements in three dimensions, In Seventh International Conference of Domain Decomposition Methods in Scientific and Engineering Computing, October 27-30, 1993, Pennsylvania State University, Contemporary Mathematics, Volume 180, (Edited by D.E. Keyes and J. Xu), pp. 99-104, AMS, (1994).
    • (1993) Seventh International Conference of Domain Decomposition Methods in Scientific and Engineering Computing , vol.180
    • Pavarino, L.F.1
  • 28
    • 0000540703 scopus 로고
    • A domain decomposition algorithm for elliptic problems in three dimensions
    • B.F. Smith, A domain decomposition algorithm for elliptic problems in three dimensions, Numer. Math. 60, 219-234 (1991).
    • (1991) Numer. Math. , vol.60 , pp. 219-234
    • Smith, B.F.1
  • 29
    • 0003881208 scopus 로고
    • Approximations spectrales de problèmes aux limites elliptiques
    • Springer-Verlag, France, Paris
    • C. Bernardi and Y. Maday, Approximations Spectrales de Problèmes aux Limites Elliptiques, Vol. 10 of Mathèmatiques & Applications, Springer-Verlag, France, Paris, (1992).
    • (1992) Mathèmatiques & Applications , vol.10
    • Bernardi, C.1    Maday, Y.2
  • 30
    • 0028450352 scopus 로고
    • Spectral element methods for large scale parallel Navier-Stokes calculations
    • Proceedings of ICOSAHOM 92, June 22-26, Montpellier, France
    • P.F. Fischer and E. Rønquist, Spectral element methods for large scale parallel Navier-Stokes calculations, In Proceedings of ICOSAHOM 92, June 22-26, 1992, Montpellier, France; Comp. Methods Appl. Mech. Eng. 116, 69-76 (1994).
    • (1992) Comp. Methods Appl. Mech. Eng. , vol.116 , pp. 69-76
    • Fischer, P.F.1    Rønquist, E.2
  • 31
    • 0000515085 scopus 로고
    • Analysis of iterative methods for the steady and unsteady stokes problem: Application of spectral element discretization
    • Y. Maday, D. Meiron, A.T. Patera and E.M. Rønquist, Analysis of iterative methods for the steady and unsteady Stokes problem: Application of spectral element discretization, SIAM J. Sci. Comp. 14, 310-337 (1993).
    • (1993) SIAM J. Sci. Comp. , vol.14 , pp. 310-337
    • Maday, Y.1    Meiron, D.2    Patera, A.T.3    Rønquist, E.M.4
  • 32
    • 0026993282 scopus 로고
    • A domain decomposition method for elliptic boundary value problems: Application to unsteady incompressible fluid flow
    • Edited by T.F. Chan, D.E. Keyes, G.A. Meurant, J.S. Scroggs and R.G. Voigt, SIAM, Philadelphia, PA
    • E.M. Rønquist, A domain decomposition method for elliptic boundary value problems: Application to unsteady incompressible fluid flow, Presented at the Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, (Edited by T.F. Chan, D.E. Keyes, G.A. Meurant, J.S. Scroggs and R.G. Voigt), SIAM, Philadelphia, PA, (1992).
    • (1992) Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations
    • Rønquist, E.M.1
  • 34
    • 0011002616 scopus 로고
    • Master's Thesis, Department of Computational and Applied Mathematics, University of Witwatersrand, Johannesburg, South Africa, December
    • S.S. Pahl, Schwarz type domain decomposition methods for spectral element discretizations, Master's Thesis, Department of Computational and Applied Mathematics, University of Witwatersrand, Johannesburg, South Africa, (December 1993).
    • (1993) Schwarz Type Domain Decomposition Methods for Spectral Element Discretizations
    • Pahl, S.S.1
  • 35
    • 0024715322 scopus 로고
    • The problem of selecting the shape functions for a p-type finite element
    • I. Babuška, M. Griebel and J. Pitkäranta, The problem of selecting the shape functions for a p-type finite element, Int. J. Numer. Meth. Eng. 28, 1891-1908 (1989).
    • (1989) Int. J. Numer. Meth. Eng. , vol.28 , pp. 1891-1908
    • Babuška, I.1    Griebel, M.2    Pitkäranta, J.3
  • 36
    • 0039035534 scopus 로고
    • The schwarz algorithm for spectral methods
    • C. Canuto and D. Funaro, The Schwarz algorithm for spectral methods, SIAM J. Numer. Anal. 25, 24-40 (1988).
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 24-40
    • Canuto, C.1    Funaro, D.2


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