메뉴 건너뛰기




Volumn 35, Issue 2, 1998, Pages 632-654

An additive schwarz method for the h-p version of the finite element method in three dimensions

Author keywords

Additive Schwarz method; Condition number; Iterative and parallel solver; The h p version

Indexed keywords


EID: 0001454480     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142996299435     Document Type: Article
Times cited : (30)

References (32)
  • 1
    • 0001146007 scopus 로고    scopus 로고
    • A preconditioner based on domain decomposition of h-p finite element approximation on quasi-uniform meshes
    • M. AINSWORTH, A preconditioner based on domain decomposition of h-p finite element approximation on quasi-uniform meshes, SIAM J. Numer. Anal., 33 (1996), pp. 1358-1376.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1358-1376
    • Ainsworth, M.1
  • 2
    • 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
  • 3
    • 0030189240 scopus 로고    scopus 로고
    • Approximation properties of the h-p version of the finite element method
    • special issue on p-and h-p version method, I. Babuška and T. Oden, eds.
    • I. BABUŠKA AND B. GUO, Approximation properties of the h-p version of the finite element method, Comput. Meth. Appl. Mech. Engrg., 133 (1996), pp. 319-346 (special issue on p-and h-p version method, I. Babuška and T. Oden, eds.).
    • (1996) Comput. Meth. Appl. Mech. Engrg. , vol.133 , pp. 319-346
    • Babuška, I.1    Guo, B.2
  • 5
    • 84968495074 scopus 로고
    • The construction of preconditioned for elliptic problems by sub structuring, IV
    • J. BRAMBLE J. PASCIAK, AND A. SCHATZ, The construction of preconditioned for elliptic problems by sub structuring, IV, Math. Comp., 53 (1989), pp. 1-24.
    • (1989) Math. Comp. , vol.53 , pp. 1-24
    • Bramble, J.1    Pasciak, J.2    Schatz, A.3
  • 7
    • 0008802864 scopus 로고
    • A Non-Nested Coarse Space for Schwarz Type Domain Decomposition Methods
    • Department of Computer Science, University of Colorado, Boulder, November
    • X. C. CAI, A Non-Nested Coarse Space for Schwarz Type Domain Decomposition Methods, Tech. report, Department of Computer Science, University of Colorado, Boulder, November 1993.
    • (1993) Tech. Report
    • Cai, X.C.1
  • 8
    • 84968491212 scopus 로고
    • Approximation results for orthogonal polynomials in Sobolev spaces
    • C. CANUTO AND A. QUARTERONI, Approximation results for orthogonal polynomials in Sobolev spaces, Math. Comp., 38 (1982), pp. 67-86.
    • (1982) Math. Comp. , vol.38 , pp. 67-86
    • Canuto, C.1    Quarteroni, A.2
  • 9
    • 0010965303 scopus 로고
    • Quasi-Optimal Schwarz Methods for the Conforming Spectral Element Discretization
    • Department of Computer Science, Courant Institute of Mathematical Science, New York University, New York
    • M. A. CASARIN, Quasi-Optimal Schwarz Methods for the Conforming Spectral Element Discretization, Tech. report 705, Department of Computer Science, Courant Institute of Mathematical Science, New York University, New York, 1995.
    • (1995) Tech. Report , vol.705
    • Casarin, M.A.1
  • 10
    • 0011029131 scopus 로고
    • Overlapping Schwarz Methods on Unstructured Meshes Using Non-Matching Coarse Grids
    • Department of Math., UCLA, Los Angeles, CA
    • T. F. CHAN, B. SMITH, AND J. ZOU, Overlapping Schwarz Methods on Unstructured Meshes Using Non-Matching Coarse Grids, CAM Reports 94-8, Department of Math., UCLA, Los Angeles, CA, 1994.
    • (1994) CAM Reports , vol.94 , Issue.8
    • Chan, T.F.1    Smith, B.2    Zou, J.3
  • 12
    • 0016541865 scopus 로고
    • Approximation by finite element functions using local regularization
    • P. CLÉMENT, Approximation by finite element functions using local regularization, RAIRO Numer. Anal., 9 (1975), pp. 77-84.
    • (1975) RAIRO Numer. Anal. , vol.9 , pp. 77-84
    • Clément, P.1
  • 13
    • 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., SIAM, Philadelphia
    • M. DRYJA, A method of domain decomposition for 3-D finite element problems, in Proc. 1st Internat. Symp. Domain Decomposition Methods for Partial Differential Equations, R. Glowinski, G. H. Golub, G. A. Meurant, and J. Périaux, eds., SIAM, Philadelphia, 1988.
    • (1988) Proc. 1st Internat. Symp. Domain Decomposition Methods for Partial Differential Equations
    • Dryja, M.1
  • 14
    • 0030556926 scopus 로고    scopus 로고
    • Multilevel Schwarz methods for elliptic problems with discontinuous coefficients in three dimensions
    • M. DRYJA, M. SAKIS, AND O. B. WIDLUND, Multilevel Schwarz methods for elliptic problems with discontinuous coefficients in three dimensions, Numer. Math., 72 (1996), pp. 313-348.
    • (1996) Numer. Math. , vol.72 , pp. 313-348
    • Dryja, M.1    Sakis, M.2    Widlund, O.B.3
  • 15
    • 0028753150 scopus 로고
    • Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions
    • M. DRYJA, B. 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.2    Widlund, O.B.3
  • 16
    • 84990712164 scopus 로고
    • Schwarz methods of Neumann-Neumann type for three-dimensional elliptic finite element problems
    • M. DRYJA AND O. B. WIDLUND, 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
    • Dryja, M.1    Widlund, O.B.2
  • 17
    • 0005708732 scopus 로고
    • The h-p version of the finite element method for solving boundary value problems in polyhedral domains
    • M. Costabel, M. Dauge, and C. Nicaise, eds., Marcel Dekker, New York, Basel
    • B. Guo, The h-p version of the finite element method for solving boundary value problems in polyhedral domains, in Boundary Value Problems and Integral Equations in Nonsmooth Domains, M. Costabel, M. Dauge, and C. Nicaise, eds., Marcel Dekker, New York, Basel, 1994, pp. 101-120.
    • (1994) Boundary Value Problems and Integral Equations in Nonsmooth Domains , pp. 101-120
    • Guo, B.1
  • 19
    • 21444453590 scopus 로고    scopus 로고
    • 3, Part 1: Countably normed spaces on polyhedral domains
    • 3, Part 1: Countably normed spaces on polyhedral domains, Proc. Roy. Soc. Edinburgh, 127 A 1997, pp. 77-126.
    • (1997) Proc. Roy. Soc. Edinburgh , vol.127 A , pp. 77-126
    • Guo, B.1    Babuška, I.2
  • 20
    • 21744441603 scopus 로고    scopus 로고
    • 3, Port 2: Regularity in neighborhoods of edges
    • 3, Port 2: Regularity in neighborhoods of edges, Proc. Roy. Soc. Edinburgh, 127 A 1997, pp. 517-545.
    • (1997) Proc. Roy. Soc. Edinburgh , vol.127 A , pp. 517-545
    • Guo, B.1    Babuška, I.2
  • 22
    • 0030493102 scopus 로고    scopus 로고
    • A preconditioner for the h-p version of the finite element method in two dimensions
    • B. GUO AND W. CAO, A preconditioner for the h-p version of the finite element method in two dimensions, Numer. Math., 75 (1996), pp. 59-77.
    • (1996) Numer. Math. , vol.75 , pp. 59-77
    • Guo, B.1    Cao, W.2
  • 23
    • 0031215985 scopus 로고    scopus 로고
    • Additive Schwarz methods for the h-p version of the finite element method in two dimensions
    • B. GUO AND W. CAO, Additive Schwarz methods for the h-p version of the finite element method in two dimensions, SIAM J. Sci. Comput., 18 (1997), pp. 1267-1288.
    • (1997) SIAM J. Sci. Comput. , vol.18 , pp. 1267-1288
    • Guo, B.1    Cao, W.2
  • 25
    • 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. J. Numer. Meth. Engrg, 29 (1990), pp. 1095-1108.
    • (1990) Internat. J. Numer. Meth. Engrg. , vol.29 , pp. 1095-1108
    • Mandel, J.1
  • 26
    • 0000587379 scopus 로고
    • Relévement de traces polynômiales et interpolations hilbertiennes entre espaces de polynômes
    • Y. MADAY. Relévement de traces polynômiales et interpolations hilbertiennes entre espaces de polynômes, C. R. Acad. Sci. Paris. Seies I, 309 (1989), pp. 463-468.
    • (1989) C. R. Acad. Sci. Paris. Seies I , vol.309 , pp. 463-468
    • Maday, Y.1
  • 27
    • 0003406818 scopus 로고
    • Domain decomposition for adaptive hp finite element methods
    • AMS
    • J. T. ODEN, A. PATRA, AND Y. S. FENG, Domain decomposition for adaptive hp finite element methods, Contemp. Mathematics, Vol. 180, AMS, 1994, pp. 295-301.
    • (1994) Contemp. Mathematics , vol.180 , pp. 295-301
    • Oden, J.T.1    Patra, A.2    Feng, Y.S.3
  • 28
    • 0000337361 scopus 로고    scopus 로고
    • A polylogarithmic bound for an iterative substructuring method for spectral elements in three dimensions
    • 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 (1996), pp. 1303-1355.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1303-1355
    • Pavarino, L.F.1    Widlund, O.B.2
  • 29
    • 0039237271 scopus 로고
    • Iterative Substructuring Methods for Spectral Elements: Problems in Three Dimensions Based on Numerical Quadrature
    • Department of Computer Science, Courant Institute of Mathematical Science, New York University, New York
    • L. F. PAVARINO AND O. B. WIDLUND, Iterative Substructuring Methods for Spectral Elements: Problems in Three Dimensions Based on Numerical Quadrature, Tech. report 663, Department of Computer Science, Courant Institute of Mathematical Science, New York University, New York, 1994.
    • (1994) Tech. Report , vol.663
    • Pavarino, L.F.1    Widlund, O.B.2
  • 31
    • 0002891427 scopus 로고
    • Iterative substructuring methods : Algorithms and theory for elliptic problems in plane
    • R. Glowinski, G.H. Golub, G.A. Meurant, J. Périaux, eds., SIAM Philadelphia, PA.
    • O. B. WIDLUND, Iterative substructuring methods : Algorithms and theory for elliptic problems in plane, in Proc. 1st Symp. Domain Decomposition Methods for Partial Differential Equations, R. Glowinski, G.H. Golub, G.A. Meurant, J. Périaux, eds., SIAM Philadelphia, PA. 1988.
    • (1988) Proc. 1st Symp. Domain Decomposition Methods for Partial Differential Equations
    • Widlund, O.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.