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Volumn 72, Issue 3, 1996, Pages 313-348

Multilevel Schwarz methods for elliptic problems with discontinuous coefficients in three dimensions

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EID: 0030556926     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110050172     Document Type: Article
Times cited : (152)

References (34)
  • 1
    • 21144473187 scopus 로고
    • A basic norm equivalence for the theory of multilevel methods
    • Bornemann, F., Yserentant, H. (1993): A basic norm equivalence for the theory of multilevel methods. Numer. Math. 64(4), 455-476
    • (1993) Numer. Math. , vol.64 , Issue.4 , pp. 455-476
    • Bornemann, F.1    Yserentant, H.2
  • 2
    • 84968468806 scopus 로고
    • New estimates for multilevel algorithms including the V -cycle
    • Bramble, J.H., Pasciak, J.E. (1993): New estimates for multilevel algorithms including the V -cycle. Math. Comp. 60, 447-471
    • (1993) Math. Comp. , vol.60 , pp. 447-471
    • Bramble, J.H.1    Pasciak, J.E.2
  • 3
    • 84968495074 scopus 로고
    • The construction of preconditioners for elliptic problems by substructuring, IV
    • Bramble, J.H., Pasciak, J.E., Schatz, A.H. (1989): The construction of preconditioners for elliptic problems by substructuring, IV. Math. Comp. 53, 1-24
    • (1989) Math. Comp. , vol.53 , pp. 1-24
    • Bramble, J.H.1    Pasciak, J.E.2    Schatz, A.H.3
  • 4
    • 84966225192 scopus 로고
    • Convergence estimates for product iterative methods with applications to domain decomposition
    • Bramble, J.H., Pasciak, J.E., Wang, J., Xu, J. (1991): Convergence estimates for product iterative methods with applications to domain decomposition. Math. Comp. 57, 1-21
    • (1991) Math. Comp. , vol.57 , pp. 1-21
    • Bramble, J.H.1    Pasciak, J.E.2    Wang, J.3    Xu, J.4
  • 5
    • 84966234195 scopus 로고
    • Parallel multilevel preconditioners
    • Bramble J.H., Pasciak, J.E., Xu, J. (1990): Parallel multilevel preconditioners. Math. Comp. 55, 1-22
    • (1990) Math. Comp. , vol.55 , pp. 1-22
    • Bramble, J.H.1    Pasciak, J.E.2    Xu, J.3
  • 10
    • 0007444976 scopus 로고
    • A method of domain decomposition for 3-D finite element problems
    • Glowinski, R., Golub, G.H., Meurant, G.A., Pénaux, J., (eds.). Philadelphia, PA, SIAM
    • Dryja, M. (1988): A method of domain decomposition for 3-D finite element problems. In: Glowinski, R., Golub, G.H., Meurant, G.A., Pénaux, J., (eds.) First International Symposium on Domain Decomposition Methods for Partial Differential Equations. Philadelphia, PA, SIAM
    • (1988) First International Symposium on Domain Decomposition Methods for Partial Differential Equations
    • Dryja, M.1
  • 11
    • 0009035387 scopus 로고
    • Multilevel methods for elliptic problems with discontinuous coefficients in three dimensions
    • Keyes, D.E., Xu, J. (eds.). AMS, Held at Penn State University, October 27-30, 1993
    • Dryja, M.: Multilevel methods for elliptic problems with discontinuous coefficients in three dimensions. In: Keyes, D.E., Xu, J. (eds.) Seventh International Conference of Domain Decomposition Methods in Scientific and Engineering Computing. AMS, 1994. Held at Penn State University, October 27-30, 1993, V. 180, 43-47
    • (1994) Seventh International Conference of Domain Decomposition Methods in Scientific and Engineering Computing , vol.180 , pp. 43-47
    • Dryja, M.1
  • 12
    • 0028753150 scopus 로고
    • Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions
    • Technical Report 638, Department of Computer Science, Courant Institute, May 1993 December
    • Dryja, M., Smith, B.F., Widlund, O.B.: Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions. Technical Report 638, Department of Computer Science, Courant Institute, May 1993. SIAM J. Numer. Anal. V. 31. (6), December 1994, 1662-1694
    • (1994) SIAM J. Numer. Anal. , vol.31 , Issue.6 , pp. 1662-1694
    • Dryja, M.1    Smith, B.F.2    Widlund, O.B.3
  • 13
    • 0006182474 scopus 로고
    • Some domain decomposition algorithms for elliptic problems
    • Hayes, L., Kincaid, D. (eds.), San Diego, California. Academic Press. Proceedings of the Conference on Iterative Methods for Large Linear Systems, held in Austin, Texas, October 19-21, 1988, to celebrate the sixty-fifth birthday of David M. Young, Jr.
    • Dryja, M., Widlund, O.B. (1989): Some domain decomposition algorithms for elliptic problems. In: Hayes, L., Kincaid, D. (eds.) Iterative Methods for Large Linear Systems, pp. 273-291, San Diego, California. Academic Press. Proceedings of the Conference on Iterative Methods for Large Linear Systems, held in Austin, Texas, October 19-21, 1988, to celebrate the sixty-fifth birthday of David M. Young, Jr.
    • (1989) Iterative Methods for Large Linear Systems , pp. 273-291
    • Dryja, M.1    Widlund, O.B.2
  • 14
    • 0002059273 scopus 로고
    • Towards a unified theory of domain decomposition algorithms for elliptic problems
    • Chan, T., Glowinski, R., Pénaux, J., Widund, O. (eds.), held in Houston, Texas, March 20-22, 1989. SIAM, Philadelphia, PA
    • Dryja, M., Widlund, O.B. (1990): Towards a unified theory of domain decomposition algorithms for elliptic problems. In: Chan, T., Glowinski, R., Pénaux, J., Widund, O. (eds.) Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, held in Houston, Texas, March 20-22, 1989. SIAM, Philadelphia, PA
    • (1990) Third International Symposium on Domain Decomposition Methods for Partial Differential Equations
    • Dryja, M.1    Widlund, O.B.2
  • 16
    • 0026978939 scopus 로고
    • Additive Schwarz methods for elliptic finite element problems in three dimensions
    • Chan, T.F., Keyes, D.E., Meurant, G.A., Scroggs, J.S., Voigt, R.G. (eds.), Phialdelphia, PA, SIAM
    • Dryja, M., Widlund, O.B. (1992): Additive Schwarz methods for elliptic finite element problems in three dimensions. In: Chan, T.F., Keyes, D.E., Meurant, G.A., Scroggs, J.S., Voigt, R.G. (eds.) Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, Phialdelphia, PA, SIAM
    • (1992) Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations
    • Dryja, M.1    Widlund, O.B.2
  • 17
    • 84990712164 scopus 로고
    • Schwarz methods of Neumann-Neumann type for three-dimensional elliptic finite element problems
    • Dryja, M., Widlund, O.B. (1995): Schwarz methods of Neumann-Neumann type for three-dimensional elliptic finite element problems. Comm. Pure Appl. Math. 48(2), 121-155
    • (1995) Comm. Pure Appl. Math. , vol.48 , Issue.2 , pp. 121-155
    • Dryja, M.1    Widlund, O.B.2
  • 22
    • 0007414360 scopus 로고
    • Two-level Schwarz methods for nonconforming finite elements and discontinuous coefficients
    • Melson, N.D., Manteuffel, T.A., McCormick, S.F. (eds.), Hampton VA. NASA
    • Sarkis, M. (1993): Two-level Schwarz methods for nonconforming finite elements and discontinuous coefficients. In: Melson, N.D., Manteuffel, T.A., McCormick, S.F. (eds.) Proceedings of the Sixth Copper Mountain Conference on Multigrid Methods, vol. 2, number 3224, pp. 543-556, Hampton VA. NASA
    • (1993) Proceedings of the Sixth Copper Mountain Conference on Multigrid Methods , vol.2 , Issue.3224 , pp. 543-556
    • Sarkis, M.1
  • 23
    • 0039216201 scopus 로고
    • 1 nonconforming finite elements and discontinuous coefficients in three dimensions
    • Keyes, D.E., Xu, J. (eds.). AMS. Held at Penn State University, October 27-30, 1993
    • 1 nonconforming finite elements and discontinuous coefficients in three dimensions. In: Keyes, D.E., Xu, J. (eds.) Seventh International Conference of Domain Decomposition Methods in Scientific and Engineering Computing. AMS. Held at Penn State University, October 27-30, 1993, V. 180, 119-124
    • (1994) Seventh International Conference of Domain Decomposition Methods in Scientific and Engineering Computing , vol.180 , pp. 119-124
    • Sarkis, M.1
  • 24
    • 0000540703 scopus 로고
    • A domain decomposition algorithm for elliptic problems in three dimensions
    • Smith, B.F. (1991). A domain decomposition algorithm for elliptic problems in three dimensions. Numer. Math. 20 (2), 219-254
    • (1991) Numer. Math. , vol.20 , Issue.2 , pp. 219-254
    • Smith, B.F.1
  • 25
    • 0005651056 scopus 로고
    • A domain decomposition algorithm using a hierarchical basis
    • Smith, B.F., Widlund, O.B. (1990): A domain decomposition algorithm using a hierarchical basis. SIAM J. Sci. Stat. Comput 11 (6), 1212-1220
    • (1990) SIAM J. Sci. Stat. Comput , vol.11 , Issue.6 , pp. 1212-1220
    • Smith, B.F.1    Widlund, O.B.2
  • 26
    • 0000846393 scopus 로고
    • A domain decomposition preconditioner based on a change to a multilevel nodal basis
    • Tong, C.H., Chan, T.F., Kuo, C.C.J. (1991): A domain decomposition preconditioner based on a change to a multilevel nodal basis. SIAM J. Sci. Stat. Comput. 12 (6), 1486-1495
    • (1991) SIAM J. Sci. Stat. Comput. , vol.12 , Issue.6 , pp. 1486-1495
    • Tong, C.H.1    Chan, T.F.2    Kuo, C.C.J.3
  • 28
    • 0039216197 scopus 로고
    • Exotic coarse spaces for Schwarz methods for lower order and spectral finite elements
    • Keyes, D.E., Xu, J. (eds.). AMS. Held at Penn State University, October 27-30, 1993
    • Widlund, O.B. (1994): Exotic coarse spaces for Schwarz methods for lower order and spectral finite elements. In: Keyes, D.E., Xu, J. (eds.) Seventh International Conference of Domain Decomposition Methods in Scientific and Engineering Computing. AMS. Held at Penn State University, October 27-30, 1993, V. 180, 131-136
    • (1994) Seventh International Conference of Domain Decomposition Methods in Scientific and Engineering Computing , vol.180 , pp. 131-136
    • Widlund, O.B.1
  • 29
    • 84966249310 scopus 로고
    • 2 projection
    • 2 projection. Math. Comp. 57, 563-568
    • (1991) Math. Comp. , vol.57 , pp. 563-568
    • Xu, J.1
  • 30
    • 0000570696 scopus 로고
    • Iterative methods by space decomposition and subspace correction
    • Xu, J. (1992): Iterative methods by space decomposition and subspace correction. SIAM Review 34(4), 581-613
    • (1992) SIAM Review , vol.34 , Issue.4 , pp. 581-613
    • Xu, J.1
  • 31
    • 0022736557 scopus 로고
    • On the multi-level splitting of finite element spaces for indefinite elliptic boundary value problems
    • Yserentant, H. (1986): On the multi-level splitting of finite element spaces for indefinite elliptic boundary value problems. SIAM J. Numer. Anal. 23, 581-595
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 581-595
    • Yserentant, H.1
  • 32
    • 0000760561 scopus 로고
    • Two preconditioners based on the multi-level splitting of finite element spaces
    • Yserentant, H. (1990): Two preconditioners based on the multi-level splitting of finite element spaces. Numer. Math. 58 (2), 163-184
    • (1990) Numer. Math. , vol.58 , Issue.2 , pp. 163-184
    • Yserentant, H.1
  • 34
    • 34249840453 scopus 로고
    • Multilevel Schwarz methods
    • Zhang, X. (1992): Multilevel Schwarz methods. Numer. Math. 63 (4), 521-539
    • (1992) Numer. Math. , vol.63 , Issue.4 , pp. 521-539
    • Zhang, X.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.