메뉴 건너뛰기




Volumn 16, Issue 10, 2009, Pages 775-799

Energy-minimizing coarse spaces for two-level Schwarz methods for multiscale PDEs

Author keywords

Coarse space; Constrained energy minimization; Domain decomposition; Overlapping additive Schwarz method; Preconditioning

Indexed keywords


EID: 70349608544     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.641     Document Type: Article
Times cited : (35)

References (33)
  • 2
    • 84974325009 scopus 로고
    • Domain decomposition algorithms
    • Cambridge University Press: Cambridge
    • Chan TF, Mathew TP. Domain decomposition algorithms. Acta Numerica. Cambridge University Press: Cambridge, 1994; 61-143.
    • (1994) Acta Numerica , pp. 61-143
    • Chan, T.F.1    Mathew, T.P.2
  • 5
    • 34548454586 scopus 로고    scopus 로고
    • Additive Schwarz with aggregation-based coarsening for elliptic problems with highly variable coefficients
    • Scheichl R, Vainikko E. Additive Schwarz with aggregation-based coarsening for elliptic problems with highly variable coefficients. Computing 2007; 80(4):319-343.
    • (2007) Computing , vol.80 , Issue.4 , pp. 319-343
    • Scheichl, R.1    Vainikko, E.2
  • 7
    • 56549108512 scopus 로고    scopus 로고
    • Coefficient-explicit Condition Number Bounds for Overlapping Additive Schwarz. Domain Decomposition Methods in Science and Engineering, XVII
    • Lecture Notes in, vol, Springer: Berlin
    • Graham IG, Scheichl R. Coefficient-explicit Condition Number Bounds for Overlapping Additive Schwarz. Domain Decomposition Methods in Science and Engineering, XVII, Lecture Notes in Computational Science and Engineering, vol. 60. Springer: Berlin, 2008; 365-372.
    • (2008) Computational Science and Engineering , vol.60 , pp. 365-372
    • Graham, I.G.1    Scheichl, R.2
  • 8
    • 0000570696 scopus 로고
    • Iterative methods by space decomposition and subspace correction
    • Xu J. Iterative methods by space decomposition and subspace correction. SIAM Reviews 1992; 34(4):581-613.
    • (1992) SIAM Reviews , vol.34 , Issue.4 , pp. 581-613
    • Xu, J.1
  • 9
    • 0033293066 scopus 로고    scopus 로고
    • An energy-minimizing interpolation for robust multigrid methods
    • Wan WL, Chan TF, Smith B. An energy-minimizing interpolation for robust multigrid methods. SIAM Journal of Scientific Computing 1999; 21(4):1632-1649.
    • (1999) SIAM Journal of Scientific Computing , vol.21 , Issue.4 , pp. 1632-1649
    • Wan, W.L.1    Chan, T.F.2    Smith, B.3
  • 10
    • 0032634013 scopus 로고    scopus 로고
    • Energy optimization of algebraic multigrid bases
    • Mandel J, Brezina M, Vaněk P. Energy optimization of algebraic multigrid bases. Computing 1999; 62(3):205-228.
    • (1999) Computing , vol.62 , Issue.3 , pp. 205-228
    • Mandel, J.1    Brezina, M.2    Vaněk, P.3
  • 11
    • 33750160340 scopus 로고    scopus 로고
    • On an energy minimizing basis for algebraic multigrid methods
    • Xu J, Zikatanov L. On an energy minimizing basis for algebraic multigrid methods. Computing and Visualization in Science 2004; 7(3-4):121-127.
    • (2004) Computing and Visualization in Science , vol.7 , Issue.3-4 , pp. 121-127
    • Xu, J.1    Zikatanov, L.2
  • 12
    • 84878786891 scopus 로고    scopus 로고
    • Algebraic Multigrid Methods Based on Compatible Relaxation and Energy Minimization. Domain Decomposition Methods in Science and Engineering, XVI
    • Springer: Berlin
    • Brannick J, Zikatanov L. Algebraic Multigrid Methods Based on Compatible Relaxation and Energy Minimization. Domain Decomposition Methods in Science and Engineering, XVI, Lecture Notes in Computational Science and Engineering, vol. 55. Springer: Berlin, 2007; 15-26.
    • (2007) Lecture Notes in Computational Science and Engineering , vol.55 , pp. 15-26
    • Brannick, J.1    Zikatanov, L.2
  • 13
    • 0001885411 scopus 로고
    • Algebraic Multigrid. Multigrid Methods, Frontiers in Applied Mathematics
    • SIAM: Philadelphia
    • Ruge JW, Stüben K. Algebraic Multigrid. Multigrid Methods, Frontiers in Applied Mathematics, vol. 3. SIAM: Philadelphia, 1987; 73-130.
    • (1987) , vol.3 , pp. 73-130
    • Ruge, J.W.1    Stüben, K.2
  • 14
    • 0030388574 scopus 로고    scopus 로고
    • Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems
    • International GAMM-Workshop on Multi-level Methods (Meisdorf, 1994)
    • Vaněk P, Mandel J, Brezina M. Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems. Computing 1996; 56(3):179-196. International GAMM-Workshop on Multi-level Methods (Meisdorf, 1994).
    • (1996) Computing , vol.56 , Issue.3 , pp. 179-196
    • Vaněk, P.1    Mandel, J.2    Brezina, M.3
  • 15
    • 0142014324 scopus 로고    scopus 로고
    • General highly accurate algebraic coarsening
    • Multilevel methods, Copper Mountain, CO
    • Brandt A. General highly accurate algebraic coarsening. Electronic Transactions on Numerical Analysis 2000; 10:1-20. Multilevel methods (Copper Mountain, CO, 1999).
    • (2000) Electronic Transactions on Numerical Analysis , vol.10 , pp. 1-20
    • Brandt, A.1
  • 18
    • 0041034172 scopus 로고    scopus 로고
    • Convergence of algebraic multigrid based on smoothed aggregation
    • Vaněk P, Brezina M, Mandel J. Convergence of algebraic multigrid based on smoothed aggregation. Numerische Mathematik 2001; 88(3):559-579.
    • (2001) Numerische Mathematik , vol.88 , Issue.3 , pp. 559-579
    • Vaněk, P.1    Brezina, M.2    Mandel, J.3
  • 23
    • 0031161210 scopus 로고    scopus 로고
    • A multiscale finite element method for elliptic problems in composite materials and porous media
    • Hou TY, Wu XH. A multiscale finite element method for elliptic problems in composite materials and porous media. Journal of Computational Physics 1997; 134(1):169-189.
    • (1997) Journal of Computational Physics , vol.134 , Issue.1 , pp. 169-189
    • Hou, T.Y.1    Wu, X.H.2
  • 24
    • 0039982148 scopus 로고    scopus 로고
    • Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients
    • Hou TY, Wu XH, Cai Z. Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. Mathematics of Computation 1999; 68(227):913-943.
    • (1999) Mathematics of Computation , vol.68 , Issue.227 , pp. 913-943
    • Hou, T.Y.1    Wu, X.H.2    Cai, Z.3
  • 25
    • 70349598862 scopus 로고    scopus 로고
    • Partition of Unity Coarse Spaces and Schwarz Methods with Harmonic Overlap. Recent Developments in Domain Decomposition Methods (Zürich, 2001)
    • Lecture Notes in, Springer: Berlin
    • Sarkis M. Partition of Unity Coarse Spaces and Schwarz Methods with Harmonic Overlap. Recent Developments in Domain Decomposition Methods (Zürich, 2001), Lecture Notes in Computational Science and Engineering, vol. 23. Springer: Berlin, 2002; 77-94.
    • (2002) Computational Science and Engineering , vol.23 , pp. 77-94
    • Sarkis, M.1
  • 26
    • 55349126017 scopus 로고    scopus 로고
    • Domain Decomposition Methods in Science and Engineering. National Autonomous University of Mexico: México
    • Sarkis M. Partition of Unity Coarse Spaces: Enhanced Versions, Discontinuous Coefficients and Applications to Elasticity. Domain Decomposition Methods in Science and Engineering. National Autonomous University of Mexico: México, 2003; 149-158.
    • (2003) Enhanced Versions, Discontinuous Coefficients and Applications to Elasticity , pp. 149-158
    • Sarkis, M.1
  • 27
    • 70349607199 scopus 로고    scopus 로고
    • Family of Energy Minimizing Coarse Spaces for Overlapping Schwarz Preconditioners
    • Domain Decomposition Methods in Science and Engineering, XVII, Lecture Notes in, Springer: Berlin
    • Dohrmann C, Klawonn A, Widlund O. A Family of Energy Minimizing Coarse Spaces for Overlapping Schwarz Preconditioners. Domain Decomposition Methods in Science and Engineering, XVII, Lecture Notes in Computational Science and Engineering, vol. 60. Springer: Berlin, 2008.
    • (2008) Computational Science and Engineering , vol.60
    • Dohrmann, C.1    Klawonn, A.2    Widlund, O.A.3
  • 28
    • 0033353559 scopus 로고    scopus 로고
    • A black-box iterative solver based on a two-level Schwarz method
    • Brezina M, Vaněk P. A black-box iterative solver based on a two-level Schwarz method. Computing 1999; 63(3):233-263.
    • (1999) Computing , vol.63 , Issue.3 , pp. 233-263
    • Brezina, M.1    Vaněk, P.2
  • 29
    • 44649112416 scopus 로고    scopus 로고
    • Compatible coarse nodal and edge elements through energy functionals
    • Musy F, Nicolas L, Perrussel R. Compatible coarse nodal and edge elements through energy functionals. SIAM Journal on Scientific Computing 2007; 29(3):1315-1337.
    • (2007) SIAM Journal on Scientific Computing , vol.29 , Issue.3 , pp. 1315-1337
    • Musy, F.1    Nicolas, L.2    Perrussel, R.3
  • 30
    • 33645748300 scopus 로고    scopus 로고
    • Multilevel upscaling through variational coarsening
    • MacLachlan SP, Moulton JD. Multilevel upscaling through variational coarsening. Water Resources Research 2006; 42(2):W02418.
    • (2006) Water Resources Research , vol.42 , Issue.2
    • MacLachlan, S.P.1    Moulton, J.D.2
  • 31
    • 0004236492 scopus 로고    scopus 로고
    • (3rd edn). Johns Hopkins University Press: Baltimore, MD
    • Golub GH, Van Loan CF. Matrix Computations (3rd edn). Johns Hopkins University Press: Baltimore, MD, 1996.
    • (1996) Matrix Computations
    • Golub, G.H.1    van Loan, C.F.2
  • 32
    • 70349602884 scopus 로고    scopus 로고
    • Gaussian user's manual
    • Kozintsev B. Gaussian user's manual. http://www.math.umd.edu/~bnk/bak/SOURCE/manual.pdf 1999.
    • (1999)
    • Kozintsev, B.1
  • 33
    • 0013079987 scopus 로고    scopus 로고
    • Parallel computation of flow in heterogeneous media modelled by mixed finite elements
    • Cliffe KA, Graham IG, Scheichl R, Stals L. Parallel computation of flow in heterogeneous media modelled by mixed finite elements. Journal of Computational Physics 2000; 164(2):258-282.
    • (2000) Journal of Computational Physics , vol.164 , Issue.2 , pp. 258-282
    • Cliffe, K.A.1    Graham, I.G.2    Scheichl, R.3    Stals, L.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.