메뉴 건너뛰기




Volumn 18, Issue 6, 1997, Pages 1676-1697

MuLTI-p preconditioners

Author keywords

Multi p preconditioner; p version of the finite element method

Indexed keywords

CONJUGATE GRADIENT METHOD; LINEAR EQUATION SOLVER; MULTI-P PRECONDITIONERS;

EID: 0031261355     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827595279368     Document Type: Article
Times cited : (15)

References (34)
  • 1
    • 0001759083 scopus 로고
    • The p-version of the finite element method
    • I. BABUSKA, B. A. SZABO, AND I. N. KATZ, The p-version of the finite element method, SIAM J. Numer. Anal., 18 (1981), pp. 515-545.
    • (1981) SIAM J. Numer. Anal. , vol.18 , pp. 515-545
    • Babuska, I.1    Szabo, B.A.2    Katz, I.N.3
  • 2
    • 0023400213 scopus 로고
    • The optimal convergence rate of the p-version of the finite element method
    • I. BABUSKA AND M. SURI, The optimal convergence rate of the p-version of the finite element method, SIAM J. Numer. Anal., 24 (1987), pp. 750-776.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 750-776
    • Babuska, I.1    Suri, M.2
  • 3
    • 0025448211 scopus 로고
    • The p- and h-p versions of the finite element method, An overview
    • I. BABUSKA AND M. SURI, The p- and h-p versions of the finite element method, An overview, Comput. Methods Appl. Mech. Engrg., 80 (1990), pp. 5-26.
    • (1990) Comput. Methods Appl. Mech. Engrg. , vol.80 , pp. 5-26
    • Babuska, I.1    Suri, M.2
  • 4
    • 0026169599 scopus 로고
    • Efficient preconditionings for the p-version of the finite element method in two dimensions
    • I. BABUSKA, A. CRAIG, J. MANDEL, AND J. PITKARANTA, Efficient preconditionings for the p-version of the 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
    • Babuska, I.1    Craig, A.2    Mandel, J.3    Pitkaranta, J.4
  • 6
    • 0024721061 scopus 로고
    • Some aspects of parallel implementation of the finite element method on message passing architectures
    • I. BABUSKA 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
    • Babuska, I.1    Elman, H.C.2
  • 7
    • 0025449042 scopus 로고
    • The h-p version of the boundary element method with geometric mesh on polygonal domains
    • I. BABUSKA, B. GUO, AND E. P. STEPHAN, The h-p version of the boundary element method with geometric mesh on polygonal domains, Comput. Methods Appl. Mech. Engrg., 74 (1990), pp. 319-325.
    • (1990) Comput. Methods Appl. Mech. Engrg. , vol.74 , pp. 319-325
    • Babuska, I.1    Guo, B.2    Stephan, E.P.3
  • 8
    • 84966199070 scopus 로고
    • The construction of preconditioners for elliptic problems by substructuring, I
    • J. H. BRAMBLE, J. E. PASCIAK, AND A. E. SCHATZ, The construction of preconditioners for elliptic problems by substructuring, I, Math. Comp., 47 (1986), pp. 103-134.
    • (1986) Math. Comp. , vol.47 , pp. 103-134
    • Bramble, J.H.1    Pasciak, J.E.2    Schatz, A.E.3
  • 9
    • 84968495074 scopus 로고
    • The construction of preconditioners for elliptic problems by substructuring, IV
    • J. H. BRAMBLE, J. E. PASCIAK, AND A. E. SCHATZ, The construction of preconditioners for elliptic problems by substructuring, 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.E.3
  • 10
    • 0024631560 scopus 로고
    • Some history of the conjugate gradient and Lanczos methods
    • G. GOLUB AND D. O'LEARY, Some history of the conjugate gradient and Lanczos methods, SIAM Rev., 31 (1989), pp. 50-102.
    • (1989) SIAM Rev. , vol.31 , pp. 50-102
    • Golub, G.1    O'Leary, D.2
  • 13
    • 0000135303 scopus 로고
    • Methods of conjugate gradients for solving linear systems
    • M. HESTERNEES AND E. STIEFEL, Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Stand., 49 (1952), pp. 409-436.
    • (1952) J. Res. Nat. Bur. Stand. , vol.49 , pp. 409-436
    • Hesternees, M.1    Stiefel, E.2
  • 14
    • 0000646657 scopus 로고
    • Multi-p methods: Iterative algorithms for the p-version of the finite element analysis
    • N. HU AND I. N. KATZ, Multi-p methods: Iterative algorithms for the p-version of the finite element analysis, SIAM J. Sci. Comput., 16 (1995), pp. 1308-1332.
    • (1995) SIAM J. Sci. Comput. , vol.16 , pp. 1308-1332
    • Hu, N.1    Katz, I.N.2
  • 16
    • 0345890601 scopus 로고
    • Block SSOR preconditionings for high order 3D FE systems, II, Incomplete BSSOR preconditionings
    • I. E. KAPOTIN, L. Y. KOLOTILINA, AND A. Y. YEREMIN, Block SSOR preconditionings for high order 3D FE systems, II, Incomplete BSSOR preconditionings, Linear Algebra Appl., 154-156 (1991), pp. 647-674.
    • (1991) Linear Algebra Appl. , vol.154-156 , pp. 647-674
    • Kapotin, I.E.1    Kolotilina, L.Y.2    Yeremin, A.Y.3
  • 17
    • 0642375971 scopus 로고
    • Block SSOR preconditionings for high order 3D FE systems
    • L. Y. KOLOTILINA AND A. Y. YEREMIN, Block SSOR preconditionings for high order 3D FE systems, BIT, 29 (1989), pp. 805-823.
    • (1989) BIT , vol.29 , pp. 805-823
    • Kolotilina, L.Y.1    Yeremin, A.Y.2
  • 19
    • 0025416211 scopus 로고
    • Two-level domain decomposition preconditioning for the p-version finite element method in three dimensions
    • J. MANDEL, Two-level domain decomposition preconditioning for the p-version finite element method in three dimensions, Internat. Numer. Methods Engrg., 29 (1990), pp. 1095-1108.
    • (1990) Internat. Numer. Methods Engrg. , vol.29 , pp. 1095-1108
    • Mandel, J.1
  • 20
    • 5944260840 scopus 로고
    • Hierarchial preconditioning and partial orthogonalization for the p-version finite element method
    • Houston, TX, T. Chan, R. Glowinski, and O. Widlund, eds., SIAM, Philadelphia, PA
    • J. MANDEL, Hierarchial preconditioning and partial orthogonalization for the p-version finite element method, in Proc. 1989 Conference on Domain Decomposition Methods, Houston, TX, T. Chan, R. Glowinski, and O. Widlund, eds., SIAM, Philadelphia, PA, 1990.
    • (1990) Proc. 1989 Conference on Domain Decomposition Methods
    • Mandel, J.1
  • 21
    • 0025449449 scopus 로고
    • Iterative solvers by substructuring for the p-version of the finite element method
    • J. MANDEL, Iterative solvers by substructuring for the p-version of the finite element method, Comput. Meth. Appl. Mech. Engrg., 80 (1990), pp. 117-128.
    • (1990) Comput. Meth. Appl. Mech. Engrg. , vol.80 , pp. 117-128
    • Mandel, J.1
  • 22
    • 0002068824 scopus 로고
    • On block diagonal and Schur complement preconditioning
    • J. MANDEL, On block diagonal and Schur complement preconditioning, Numer. Math., 58 (1990), pp. 79-93.
    • (1990) Numer. Math. , vol.58 , pp. 79-93
    • Mandel, J.1
  • 24
    • 0000955614 scopus 로고
    • Variational multigrid theory
    • Multigrid Methods, S. F. McCormick, ed., SIAM, Philadelphia, PA
    • J. MANDEL, S. F. MCCORMICK, AND R. E. BANK, Variational multigrid theory, in Multigrid Methods, S. F. McCormick, ed., Frontiers in Applied Mathematics 3, SIAM, Philadelphia, PA, 1987, pp. 131-177.
    • (1987) Frontiers in Applied Mathematics , vol.3 , pp. 131-177
    • Mandel, J.1    Mccormick, S.F.2    Bank, R.E.3
  • 25
    • 0001685657 scopus 로고
    • An algebraic interpretation of multigrid methods
    • S. F. MCCORMICK, An algebraic interpretation of multigrid methods, SIAM J. Numer. Anal., 19 (1982), pp. 548-560.
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 548-560
    • Mccormick, S.F.1
  • 26
    • 0021417959 scopus 로고
    • Multigrid methods for variational problems: Further results
    • S. F. MCCORMICK, Multigrid methods for variational problems: further results, SIAM J. Numer. Anal., 21 (1984), pp. 255-263.
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 255-263
    • Mccormick, S.F.1
  • 27
    • 0021478985 scopus 로고
    • Multigrid methods: Convergence theory in a variational framework
    • J. F. MAITRE AND F. MUSY, Multigrid methods: Convergence theory in a variational framework, SIAM J. Numer. Anal., 21 (1984), pp. 657-671.
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 657-671
    • Maitre, J.F.1    Musy, F.2
  • 28
    • 0343959849 scopus 로고
    • Algebraic Normalization of the multigrid method in the symmetric and positive definite case - A convergence estimation for the V-cycle
    • D. J. Paddon and H. Holstein, eds., Institute of Mathematics and Its Applications Conference Series 3, Clarendon Press, Oxford, UK
    • J. F. MAITRE AND F. MUSY, Algebraic Normalization of the multigrid method in the symmetric and positive definite case - a convergence estimation for the V-cycle, in Multigrid Methods for Integral and Differential Equations, D. J. Paddon and H. Holstein, eds., Institute of Mathematics and Its Applications Conference Series 3, Clarendon Press, Oxford, UK, 1985, pp. 213-224.
    • (1985) Multigrid Methods for Integral and Differential Equations , pp. 213-224
    • Maitre, J.F.1    Musy, F.2
  • 30
    • 0000570696 scopus 로고
    • Iterative methods by space decomposition and subspace correction
    • J. Xu, Iterative methods by space decomposition and subspace correction, SIAM Rev., 4 (1992), pp. 581-613.
    • (1992) SIAM Rev. , vol.4 , pp. 581-613
    • Xu, J.1
  • 31
    • 34250126304 scopus 로고
    • On the multi-level splitting of finite element spaces
    • H. YSBRENTANT, On the multi-level splitting of finite element spaces, Numer. Math., 49 (1986), pp. 379-412.
    • (1986) Numer. Math. , vol.49 , pp. 379-412
    • Ysbrentant, H.1
  • 32
    • 85033290802 scopus 로고
    • Engineering Software Research and Development, Inc., St. Louis, MO
    • STRESS CHECK, User's Manual, Engineering Software Research and Development, Inc., St. Louis, MO, 1994; also available online from http://www.ESRD.com/.
    • (1994) STRESS CHECK, User's Manual
  • 34
    • 85033287065 scopus 로고
    • Solvers International, Inc., Boulder, CO
    • ROCKITS, Solvers International, Inc., Boulder, CO, 1994.
    • (1994) ROCKITS


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.