메뉴 건너뛰기




Volumn 15, Issue 2-3 SPEC. ISS., 2008, Pages 271-289

Domain decomposition preconditioners for elliptic equations with jump coefficients

Author keywords

Conjugate gradient; Domain decomposition; Effective condition number; Jump coefficients

Indexed keywords


EID: 51449115842     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.566     Document Type: Conference Paper
Times cited : (27)

References (41)
  • 3
    • 0000035075 scopus 로고    scopus 로고
    • An efficient preconditioned CG method for the solution of a class of layered problems with extreme contrasts in the coefficients
    • Vuik C, Segal A, Meijerink JA. An efficient preconditioned CG method for the solution of a class of layered problems with extreme contrasts in the coefficients. Journal of Computational Physics 1999; 152(1 ):385-403.
    • (1999) Journal of Computational Physics , vol.152 , Issue.1 , pp. 385-403
    • Vuik, C.1    Segal, A.2    Meijerink, J.A.3
  • 4
    • 0030409471 scopus 로고    scopus 로고
    • Parallel solvers for linear and nonlinear exterior magnetic field problems based upon coupled FE/BE formulations
    • Heise B, Kuhn M. Parallel solvers for linear and nonlinear exterior magnetic field problems based upon coupled FE/BE formulations. Computing 1996; 56(3):237-258.
    • (1996) Computing , vol.56 , Issue.3 , pp. 237-258
    • Heise, B.1    Kuhn, M.2
  • 5
    • 0029733560 scopus 로고    scopus 로고
    • Massively parallel methods for semiconductor device modelling
    • Coomer RK, Graham IG. Massively parallel methods for semiconductor device modelling. Computing 1996; 56(1): 1-27.
    • (1996) Computing , vol.56 , Issue.1 , pp. 1-27
    • Coomer, R.K.1    Graham, I.G.2
  • 6
    • 27144454570 scopus 로고    scopus 로고
    • An iterative method for solving complex-symmetric systems arising in electrical power modeling
    • Howie VE, Vavasis SA. An iterative method for solving complex-symmetric systems arising in electrical power modeling. SIAM Journal on Matrix Analysis and Applications 2005; 26(4):1150-1178.
    • (2005) SIAM Journal on Matrix Analysis and Applications , vol.26 , Issue.4 , pp. 1150-1178
    • Howie, V.E.1    Vavasis, S.A.2
  • 7
    • 7544231743 scopus 로고    scopus 로고
    • Fundamental models for fuel cell engineering
    • Wang C. Fundamental models for fuel cell engineering. Chemical Reviews 2004; 104:4727-4766.
    • (2004) Chemical Reviews , vol.104 , pp. 4727-4766
    • Wang, C.1
  • 8
    • 0035250720 scopus 로고    scopus 로고
    • Two phase flow and transport in the air cathode of proton exchange membrane fuel cells
    • Wang Z, Wang C. Chen K. Two phase flow and transport in the air cathode of proton exchange membrane fuel cells. Journal of Power Sources 2001; 94:40-50.
    • (2001) Journal of Power Sources , vol.94 , pp. 40-50
    • Wang, Z.1    Wang, C.2    Chen, K.3
  • 9
    • 84968495074 scopus 로고
    • The construction of preconditioners for elliptic problems by substructuring. IV
    • Bramble JH, Pasciak JE, Schatz AH. The construction of preconditioners for elliptic problems by substructuring. IV. Mathematics of Computation 1989; 53(187): 1-24.
    • (1989) Mathematics of Computation , vol.53 , Issue.187 , pp. 1-24
    • Bramble, J.H.1    Pasciak, J.E.2    Schatz, A.H.3
  • 10
    • 0034322884 scopus 로고    scopus 로고
    • Robust multigrid methods for nonsmooth coefficient elliptic linear systems
    • Chan T, Wan W. Robust multigrid methods for nonsmooth coefficient elliptic linear systems. Journal of Computational and Applied Mathematics 2000; 123:323-352.
    • (2000) Journal of Computational and Applied Mathematics , vol.123 , pp. 323-352
    • Chan, T.1    Wan, W.2
  • 11
    • 84990712164 scopus 로고
    • Schwarz methods of Neumann-Neumann type for three-dimensional elliptic finite element problems
    • Dryja M, Widlund OB. Schwarz methods of Neumann-Neumann type for three-dimensional elliptic finite element problems. Communications on Pure and Applied Mathematics 1995; 48(2): 121-155.
    • (1995) Communications on Pure and Applied Mathematics , vol.48 , Issue.2 , pp. 121-155
    • Dryja, M.1    Widlund, O.B.2
  • 12
    • 0030518529 scopus 로고    scopus 로고
    • Balancing domain decomposition for problems with large jumps in coefficients
    • Mandel J, Brezina M. Balancing domain decomposition for problems with large jumps in coefficients. Mathematics of Computation 1996; 65(216): 1387-1401.
    • (1996) Mathematics of Computation , vol.65 , Issue.216 , pp. 1387-1401
    • Mandel, J.1    Brezina, M.2
  • 13
    • 0000540703 scopus 로고
    • A domain decomposition algorithm for elliptic problems in three dimensions
    • Smith BF. A domain decomposition algorithm for elliptic problems in three dimensions. Numerische Mathematik 1991; 60(2):219-234.
    • (1991) Numerische Mathematik , vol.60 , Issue.2 , pp. 219-234
    • Smith, B.F.1
  • 14
    • 0032290868 scopus 로고    scopus 로고
    • Some nonoverlapping domain decomposition methods
    • electronic
    • Xu J, Zou J. Some nonoverlapping domain decomposition methods. SIAM Review 1998; 40(4):857-914 (electronic).
    • (1998) SIAM Review , vol.40 , Issue.4 , pp. 857-914
    • Xu, J.1    Zou, J.2
  • 15
    • 84966211313 scopus 로고
    • The construction of preconditioners for elliptic problems by substructuring. III
    • Bramble JH, Pasciak JE, Schatz AH. The construction of preconditioners for elliptic problems by substructuring. III. Mathematics of Computation 1988; 51(184):415-430.
    • (1988) Mathematics of Computation , vol.51 , Issue.184 , pp. 415-430
    • Bramble, J.H.1    Pasciak, J.E.2    Schatz, A.H.3
  • 16
    • 51449088560 scopus 로고    scopus 로고
    • Technical Report rep05-22
    • Radon Institute for Computational and Applied Mathematics RICAM
    • Cho S, Nepomnyaschikh SV, Park E-J. Domain decomposition preconditioning for elliptic problems with jumps in coefficients. Technical Report rep05-22, Radon Institute for Computational and Applied Mathematics (RICAM), 2005.
    • (2005)
    • Cho, S.1    Nepomnyaschikh, S.V.2    Park, E.-J.3
  • 18
    • 43949128484 scopus 로고
    • Domain decomposition for elliptic problems with large jumps in coefficients
    • National Defense Industry Press: Beijing. China
    • Wang J, Xie R. Domain decomposition for elliptic problems with large jumps in coefficients. Proceedings of Conference on Scientific and Engineering Computing. National Defense Industry Press: Beijing. China, 1994; 74-86.
    • (1994) Proceedings of Conference on Scientific and Engineering Computing , pp. 74-86
    • Wang, J.1    Xie, R.2
  • 19
    • 84966255975 scopus 로고
    • Convergence estimates for multigrid algorithms without regularity assumption
    • Bramble JH, Pasciak JE, Wang J, Xu J. Convergence estimates for multigrid algorithms without regularity assumption. Mathematics of Computation 1991; 57(195):23-45.
    • (1991) Mathematics of Computation , vol.57 , Issue.195 , pp. 23-45
    • Bramble, J.H.1    Pasciak, J.E.2    Wang, J.3    Xu, J.4
  • 20
    • 0000570696 scopus 로고
    • Iterative methods by space decomposition and subspace correction
    • Xu J. Iterative methods by space decomposition and subspace correction. SIAM Review 1992; 34:581-613.
    • (1992) SIAM Review , vol.34 , pp. 581-613
    • Xu, J.1
  • 21
    • 0028369940 scopus 로고
    • Domain decomposition methods in computational mechanics
    • Le Tallec P. Domain decomposition methods in computational mechanics. Computational Mechanics Advances 1994; 1(2): 121-220.
    • (1994) Computational Mechanics Advances , vol.1 , Issue.2 , pp. 121-220
    • Le Tallec, P.1
  • 24
    • 0033447331 scopus 로고    scopus 로고
    • On the robustness of the BPX-preconditioner with respect to jumps in the coefficients
    • Oswald P. On the robustness of the BPX-preconditioner with respect to jumps in the coefficients. Mathematics of Computation 1999; 68:633-650.
    • (1999) Mathematics of Computation , vol.68 , pp. 633-650
    • Oswald, P.1
  • 25
    • 43949151026 scopus 로고
    • New convergence estimates for multilevel algorithms for finite-element approximations
    • l-3:593-604
    • Wang J. New convergence estimates for multilevel algorithms for finite-element approximations. Journal of Computational and Applied Mathematics 1994; 50(l-3):593-604.
    • (1994) Journal of Computational and Applied Mathematics , vol.50
    • Wang, J.1
  • 26
    • 0030556926 scopus 로고    scopus 로고
    • Multilevel Schwarz methods for elliptic problems with discontinuous coefficients in three dimensions
    • Dryja M, Sarkis MV, Widlund OB. Multilevel Schwarz methods for elliptic problems with discontinuous coefficients in three dimensions. Numerische Mathematik 1996; 72(3):313-348.
    • (1996) Numerische Mathematik , vol.72 , Issue.3 , pp. 313-348
    • Dryja, M.1    Sarkis, M.V.2    Widlund, O.B.3
  • 27
    • 0028753150 scopus 로고
    • Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions
    • Dryja M, Smith BF, Widlund OB. Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions. SIAM Journal on Numerical Analysis 1994; 31(6): 1662-1694.
    • (1994) SIAM Journal on Numerical Analysis , vol.31 , Issue.6 , pp. 1662-1694
    • Dryja, M.1    Smith, B.F.2    Widlund, O.B.3
  • 29
    • 43949119877 scopus 로고    scopus 로고
    • Multilevel preconditioners for elliptic equations with jump coefficients on bisection grids
    • preprint
    • Xu J, Zhu Y. Multilevel preconditioners for elliptic equations with jump coefficients on bisection grids. 2007, preprint.
    • (2007)
    • Xu, J.1    Zhu, Y.2
  • 30
    • 43949139588 scopus 로고    scopus 로고
    • Uniform convergent multigrid methods for elliptic problems with strongly discontinuous coefficients
    • Xu J, Zhu Y. Uniform convergent multigrid methods for elliptic problems with strongly discontinuous coefficients. Mathematical Models and Methods in Applied Sciences 2008; 18(2): 1-29.
    • (2008) Mathematical Models and Methods in Applied Sciences , vol.18 , Issue.2 , pp. 1-29
    • Xu, J.1    Zhu, Y.2
  • 31
    • 0033295349 scopus 로고    scopus 로고
    • Unstructured additive Schwarz-conjugate gradient method for elliptic problems with highly discontinuous coefficients
    • Graham IG, Hagger MJ. Unstructured additive Schwarz-conjugate gradient method for elliptic problems with highly discontinuous coefficients. SIAM Journal on Scientific Computing 1999; 20:2041-2066.
    • (1999) SIAM Journal on Scientific Computing , vol.20 , pp. 2041-2066
    • Graham, I.G.1    Hagger, M.J.2
  • 32
    • 0037472514 scopus 로고    scopus 로고
    • Iteration number for the conjugate gradient method
    • Axelsson O. Iteration number for the conjugate gradient method. Mathematics and Computers in Simulation 2003; 61(3-6):421-435.
    • (2003) Mathematics and Computers in Simulation , vol.61 , Issue.3-6 , pp. 421-435
    • Axelsson, O.1
  • 39
    • 84974325009 scopus 로고
    • Domain decomposition algorithms
    • Chan TF, Mathew TP. Domain decomposition algorithms. Acta Numerica 1994; 3:61-143.
    • (1994) Acta Numerica , vol.3 , pp. 61-143
    • Chan, T.F.1    Mathew, T.P.2
  • 41
    • 34249840453 scopus 로고
    • Multilevel Schwarz methods
    • Zhang X. Multilevel Schwarz methods. Numerische Mathematik 1992; 63(1):521-539.
    • (1992) Numerische Mathematik , vol.63 , Issue.1 , pp. 521-539
    • Zhang, X.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.