메뉴 건너뛰기




Volumn 33, Issue 4, 1996, Pages 1303-1335

A polylogarithmic bound for an iterative substructuring method for spectral elements in three dimensions

Author keywords

Domain decomposition; Iterative substructuring; p version finite elements; Spectral approximation

Indexed keywords


EID: 0000337361     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142994265176     Document Type: Article
Times cited : (75)

References (54)
  • 1
    • 0026169599 scopus 로고
    • Efficient preconditioning for the p-version finite element method in two dimensions
    • I. BABUŠKA, A. CRAIG, J. MANDEL, AND J. PITKÄRANTA, Efficient preconditioning for the p-version finite element method in two dimensions. SIAM J. Numer. Anal., 28 (1991), pp. 624-661.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 624-661
    • Babuška, I.1    Craig, A.2    Mandel, J.3    Pitkäranta, J.4
  • 2
    • 0024721061 scopus 로고
    • Some aspects of parallel implementation of the finite-element method on message passing architectures
    • I. BABUŠKA AND H. C. ELMAN, Some aspects of parallel implementation of the finite-element method on message passing architectures. J. Comput. Appl. Math., 27 (1989), pp. 157-187.
    • (1989) J. Comput. Appl. Math. , vol.27 , pp. 157-187
    • Babuška, I.1    Elman, H.C.2
  • 3
    • 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, Internat. J. Numer. Methods Engrg., 28 (1989), pp. 1891-1908.
    • (1989) Internat. J. Numer. Methods Engrg. , vol.28 , pp. 1891-1908
    • Babuška, I.1    Griebel, M.2    Pitkäranta, J.3
  • 4
    • 0039633136 scopus 로고
    • A note on an inequality of E. Schmidt
    • R. BELLMAN, A note on an inequality of E. Schmidt. Bull. Amer. Math. Soc., 50 (1944), pp. 734-736.
    • (1944) Bull. Amer. Math. Soc. , vol.50 , pp. 734-736
    • Bellman, R.1
  • 5
    • 85033762334 scopus 로고
    • Relèvement Polynômiaux sur un Cube
    • Electricité de France, Paris, France
    • F. BEN BELGACEM, Relèvement Polynômiaux sur un Cube, Technical Report HI-72/7780, Electricité de France, Paris, France, 1992.
    • (1992) Technical Report HI-72/7780
    • Ben Belgacem, F.1
  • 7
    • 0038914038 scopus 로고
    • Relèvement polynomial de traces et applications
    • _, Relèvement polynomial de traces et applications, RAIRO Modél. Mat. Anal. Numér., 24 (1990), pp. 557-611.
    • (1990) RAIRO Modél. Mat. Anal. Numér. , vol.24 , pp. 557-611
  • 8
    • 0346179710 scopus 로고
    • Parallel domain decomposition and iterative refinement algorithms
    • Parallel Algorithms for PDEs, Wolfgang Hackbusch, ed., Vieweg-Verlag, Braunschweig, Wiesbaden
    • P. E. BJØRSTAD, R. MOE, AND M. SKOGEN, Parallel domain decomposition and iterative refinement algorithms, in Parallel Algorithms for PDEs, Proceedings of the 6th GAMM-Seminar, Wolfgang Hackbusch, ed., Vieweg-Verlag, Braunschweig, Wiesbaden, 1990.
    • (1990) Proceedings of the 6th GAMM-Seminar
    • Bjørstad, P.E.1    Moe, R.2    Skogen, M.3
  • 9
    • 0026964009 scopus 로고
    • Domain decomposition algorithms of Schwarz type, designed for massively parallel computers
    • T. F. Chan et al., eds., Society for Industrial and Applied Mathematics, Philadelphia, PA
    • P. E. BJØRSTAD AND M. SKOGEN, Domain decomposition algorithms of Schwarz type, designed for massively parallel computers, in Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, T. F. Chan et al., eds., Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992.
    • (1992) Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations
    • Bjørstad, P.E.1    Skogen, M.2
  • 10
    • 84968495074 scopus 로고
    • The construction of preconditioners for elliptic problems by substructures, IV
    • J. H. BRAMBLE, J. E. PASCIAK, AND A. H. SCHATZ, The construction of preconditioners for elliptic problems by substructures, IV, Math. Comp., 53 (1989), pp. 1-24.
    • (1989) Math. Comp. , vol.53 , pp. 1-24
    • Bramble, J.H.1    Pasciak, J.E.2    Schatz, A.H.3
  • 12
    • 0026976848 scopus 로고
    • A comparison of some domain decomposition algorithms for nonsymmetric elliptic problems
    • T. F. Chan et al., eds., Society for Industrial and Applied Mathematics, 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, T. F. Chan et al., eds., Society for Industrial and Applied Mathematics, 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
  • 13
    • 84985341546 scopus 로고
    • A comparison of some domain decomposition and ILU preconditioned iterative methods for nonsymmetric elliptic problems
    • _, A comparison of some domain decomposition and ILU preconditioned iterative methods for nonsymmetric elliptic problems, J. Numer. Linear Algebra Appl., 1 (1994), pp. 477-504.
    • (1994) J. Numer. Linear Algebra Appl. , vol.1 , pp. 477-504
  • 14
    • 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 (1988), pp. 24-40.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 24-40
    • Canuto, C.1    Funaro, D.2
  • 18
    • 21844508844 scopus 로고
    • Balancing domain decomposition for mixed finite elements
    • L. C. COWSAR, J. MANDEL, AND M. F. WHEELER, Balancing domain decomposition for mixed finite elements, Math. Comp., 64 (1995), pp. 989-1015.
    • (1995) Math. Comp. , vol.64 , pp. 989-1015
    • Cowsar, L.C.1    Mandel, J.2    Wheeler, M.F.3
  • 19
    • 0007444976 scopus 로고
    • A method of domain decomposition for 3-D finite element problems
    • R. Glowinski, G. H. Golub, G. A. Meurant, and J. Périaux, eds., Society for Industrial and Applied Mathematics, Philadelphia, PA
    • M. DRYJA, A method of domain decomposition for 3-D finite element problems, in First International Symposium on Domain Decomposition Methods for Partial Differential Equations, R. Glowinski, G. H. Golub, G. A. Meurant, and J. Périaux, eds., Society for Industrial and Applied Mathematics, Philadelphia, PA, 1988.
    • (1988) First International Symposium on Domain Decomposition Methods for Partial Differential Equations
    • Dryja, M.1
  • 20
    • 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
  • 21
    • 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
  • 22
    • 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
  • 23
    • 85033750828 scopus 로고
    • Some recent results on Schwarz type domain decomposition algorithms
    • Y. A. Kuznetsov, J. Périaux, A. Quarteroni, and O. B. Widlund, eds., American Mathematical Society, Providence, RI
    • _, Some recent results on Schwarz type domain decomposition algorithms, in Sixth Conference on Domain Decomposition Methods for Partial Differential Equations, Y. A. Kuznetsov, J. Périaux, A. Quarteroni, and O. B. Widlund, eds., American Mathematical Society, Providence, RI, 1994.
    • (1994) Sixth Conference on Domain Decomposition Methods for Partial Differential Equations
  • 24
    • 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
  • 25
    • 0028450352 scopus 로고
    • Spectral element methods for large scale parallel Navier-Stokes calculations
    • P. F. FISCHER AND E. RØNQUIST, Spectral element methods for large scale parallel Navier-Stokes calculations, Comput. Methods Appl. Mech. Engrg., 116 (1994), pp. 69-76.
    • (1994) Comput. Methods Appl. Mech. Engrg. , vol.116 , pp. 69-76
    • Fischer, P.F.1    Rønquist, E.2
  • 30
    • 0042468730 scopus 로고
    • Experiences with domain decomposition in three dimensions: Overlapping Schwarz methods
    • Y. A. Kuznetsov, J. Périaux, A. Quarteroni, and O. B. Widlund, eds., American Mathematical Society, Providence, RI
    • W. D. GROPP AND B. F. SMITH, Experiences with domain decomposition in three dimensions: Overlapping Schwarz methods, in Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition, Y. A. Kuznetsov, J. Périaux, A. Quarteroni, and O. B. Widlund, eds., American Mathematical Society, Providence, RI, 1994.
    • (1994) Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition
    • Gropp, W.D.1    Smith, B.F.2
  • 34
    • 0000587379 scopus 로고
    • Relèvement de traces polynomials et interpolations hilbertiennes entre espaces de polynômes
    • Série I
    • Y. MADAY, Relèvement de traces polynomials et interpolations hilbertiennes entre espaces de polynômes, C. R. Acad. Sci. Paris, Série I, 309 (1989), pp. 463-468.
    • (1989) C. R. Acad. Sci. Paris , vol.309 , pp. 463-468
    • Maday, Y.1
  • 35
    • 0024917277 scopus 로고
    • Spectral element methods for the Navier-Stokes equations
    • A. K. Noor and J. T. Oden, eds., ASME, New York
    • Y. MADAY AND A. T. PATERA, Spectral element methods for the Navier-Stokes equations, in State of the Art Surveys in Computational Mechanics, A. K. Noor and J. T. Oden, eds., ASME, New York, 1989.
    • (1989) State of the Art Surveys in Computational Mechanics
    • Maday, Y.1    Patera, A.T.2
  • 37
    • 0002738072 scopus 로고
    • Hierarchical preconditioning and partial orthogonalization for the p-version finite element method
    • T. F. Chan, R. Glowinski, J. Périaux, and O. Widlund, eds., Society for Industrial and Applied Mathematics, Philadelphia, PA
    • _, Hierarchical preconditioning and partial orthogonalization for the p-version finite element method, in Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, T. F. 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
  • 38
    • 0042499568 scopus 로고
    • Intelligent block iterative methods
    • Monte Carlo, November 1993, J. Robinson, ed., Robinson Associates, Ltd., Okehampton, Devon, England
    • _, Intelligent block iterative methods, in Proceedings of the 7th World Congress on Finite Elements, Monte Carlo, November 1993, J. Robinson, ed., Robinson Associates, Ltd., Okehampton, Devon, England, 1993, pp. 471-477.
    • (1993) Proceedings of the 7th World Congress on Finite Elements , pp. 471-477
  • 39
    • 0025449449 scopus 로고
    • Iterative solvers by substructuring for the p-version finite element method
    • _, Iterative solvers by substructuring for the p-version finite element method, Comput. Methods Appl. Mech. Engrg., 80 (1990), pp. 117-128.
    • (1990) Comput. Methods Appl. Mech. Engrg. , vol.80 , pp. 117-128
  • 40
    • 0028447775 scopus 로고
    • Iterative solvers for p-version finite element method in three dimensions
    • _, Iterative solvers for p-version finite element method in three dimensions, Comput. Methods Appl. Mech. Engrg., 116 (1994), pp. 175-183.
    • (1994) Comput. Methods Appl. Mech. Engrg. , vol.116 , pp. 175-183
  • 41
    • 0025416211 scopus 로고
    • Two-level domain decomposition preconditioning for the p-version finite element version in three dimensions
    • _, Two-level domain decomposition preconditioning for the p-version finite element version in three dimensions, Internat. J. Numer. Methods Engrg., 29 (1990), pp. 1095-1108.
    • (1990) Internat. J. Numer. Methods Engrg. , vol.29 , pp. 1095-1108
  • 42
    • 0011002616 scopus 로고
    • Master's thesis, Department of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa
    • S. S. PAHL, Schwarz Type Domain Decomposition Methods for Spectral Element Discretizations, Master's thesis, Department of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa, 1993.
    • (1993) Schwarz Type Domain Decomposition Methods for Spectral Element Discretizations
    • Pahl, S.S.1
  • 43
    • 21344476056 scopus 로고
    • Additive Schwarz methods for the p-version finite element method
    • L. F. PAVARINO, Additive Schwarz methods for the p-version finite element method, Numer. Math., 66 (1994), pp. 493-515.
    • (1994) Numer. Math. , vol.66 , pp. 493-515
    • Pavarino, L.F.1
  • 45
    • 85033757154 scopus 로고
    • A wire basket based method for spectral elements in three dimensions
    • D. E. Keyes and J. Xu, eds., American Mathematical Society, Providence, RI
    • _, A wire basket based method for spectral elements in three dimensions, in Seventh International Conference of Domain Decomposition Methods in Scientific and Engineering Computing, D. E. Keyes and J. Xu, eds., American Mathematical Society, Providence, RI, 1994.
    • (1994) Seventh International Conference of Domain Decomposition Methods in Scientific and Engineering Computing
  • 46
    • 0041025990 scopus 로고
    • Iterative Substructuring Methods for Spectral Elements in Three Dimensions
    • M. Křižek and P. Neittaanmäki, eds., Marcel Dekker, New York, Basel, Hong Kong
    • L. F. PAVARINO AND O. B. WIDLUND, Iterative Substructuring Methods for Spectral Elements in Three Dimensions, in Proceedings of FEM50 The Finite Element Method: Fifty Years of the Courant Element, M. Křižek and P. Neittaanmäki, eds., Marcel Dekker, New York, Basel, Hong Kong, 1994, pp. 345-355.
    • (1994) Proceedings of FEM50 the Finite Element Method: Fifty Years of the Courant Element , pp. 345-355
    • Pavarino, L.F.1    Widlund, O.B.2
  • 47
    • 0039237271 scopus 로고
    • Iterative Substructuring Methods for Spectral Elements: Problems in Three Dimensions Based on Numerical Quadrature
    • Technical Report 663, Department of Computer Science, Courant Institute of Mathematical Sciences, New York University, New York, NY, to appear
    • _, Iterative Substructuring Methods for Spectral Elements: Problems in Three Dimensions Based on Numerical Quadrature, Technical Report 663, Department of Computer Science, Courant Institute of Mathematical Sciences, New York University, New York, NY, 1994. Comput. Math. Appl., to appear.
    • (1994) Comput. Math. Appl.
  • 49
    • 0026993282 scopus 로고
    • A domain decomposition method for elliptic boundary value problems: Application to unsteady incompressible fluid flow
    • T. F. Chan et al., eds., Society for Industrial and Applied Mathematics, Philadelphia, PA
    • E. M. RØNQUIST, A domain decomposition method for elliptic boundary value problems: Application to unsteady incompressible fluid flow, in Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations. T. F. Chan et al., eds., Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992.
    • (1992) Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations
    • Rønquist, E.M.1
  • 51
    • 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 (1991), pp. 219-234.
    • (1991) Numer. Math. , vol.60 , pp. 219-234
    • Smith, B.F.1
  • 53
    • 0003559010 scopus 로고
    • A parallel implementation of an iterative substructuring algorithm for problems in three dimensions
    • _, A parallel implementation of an iterative substructuring algorithm for problems in three dimensions, SIAM J. Sci. Comput., 14 (1993), pp. 406-423.
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 406-423
  • 54


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.