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Volumn 77, Issue 4, 2006, Pages 347-377

An algebraic multigrid method for higher-order finite element discretizations

Author keywords

Algebraic multigrid methods; Geometric based; High order finite element; Unstructured grids

Indexed keywords

ALGEBRAIC MULTIGRID METHODS; GEOMETRIC-BASED; HIGH-ORDER FINITE ELEMENT; UNSTRUCTURED GRIDS;

EID: 33745637010     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00607-006-0162-6     Document Type: Article
Times cited : (25)

References (27)
  • 1
    • 0030527614 scopus 로고    scopus 로고
    • An algorithm for coarsing unstructured meshes
    • Bank, R., Xu, J.: An algorithm for coarsing unstructured meshes. Numer. Math. 73(1), 1-36 (1996).
    • (1996) Numer. Math. , vol.73 , Issue.1 , pp. 1-36
    • Bank, R.1    Xu, J.2
  • 2
    • 84966255975 scopus 로고
    • Convergence estimates for multigrid algorithms without regularity assumptions
    • Bramble, J. H., Pasciak, J. E., Wang, J., Xu, J.: Convergence estimates for multigrid algorithms without regularity assumptions. Math. Comp. 57(195), 23-45 (1991).
    • (1991) Math. Comp. , vol.57 , Issue.195 , pp. 23-45
    • Bramble, J.H.1    Pasciak, J.E.2    Wang, J.3    Xu, J.4
  • 3
    • 84966233568 scopus 로고
    • Multi-level adaptive solutions to boundary-value problems
    • Brandt, A.: Multi-level adaptive solutions to boundary-value problems. Math. Comp. 31, 333-390 (1977).
    • (1977) Math. Comp. , vol.31 , pp. 333-390
    • Brandt, A.1
  • 6
    • 15944372444 scopus 로고
    • Sparsity and its application (Evans, D. J., ed.). Cambridge: Cambridge University Press
    • Brandt, A.: Algebraic multigrid (AMG) for sparse matrix equations. In: Sparsity and its application (Evans, D. J., ed.). Cambridge: Cambridge University Press 1984.
    • (1984) Algebraic Multigrid (AMG) for Sparse Matrix Equations.
    • Brandt, A.1
  • 11
    • 0001677218 scopus 로고
    • Black box multigrid
    • Dendy, J. E.: Black box multigrid. J. Comput. Phys. 48, 366-386 (1982).
    • (1982) J. Comput. Phys. , vol.48 , pp. 366-386
    • Dendy, J.E.1
  • 12
    • 0000713961 scopus 로고    scopus 로고
    • Convergence of a non-conforming multiscale finite element method
    • electronic
    • Efendiev, Y. R., Hou, T. Y., Wu, Z.-H.: Convergence of a non-conforming multiscale finite element method. SIAM J. Numer. Anal. 37(3), 888-910 (electronic) (2000).
    • (2000) SIAM J. Numer. Anal. , vol.37 , Issue.3 , pp. 888-910
    • Efendiev, Y.R.1    Hou, T.Y.2    Wu, Z.-H.3
  • 13
    • 0003360974 scopus 로고
    • Multigrid methods and applications
    • Berlin: Springer
    • Hackbusch, W.: Multigrid methods and applications. Computational Mathematics, vol. 4. Berlin: Springer 1985.
    • (1985) Computational Mathematics , vol.4
    • Hackbusch, W.1
  • 14
    • 0036226531 scopus 로고    scopus 로고
    • Element-free AMGe: General algorithms for computing interpolation weights in AMG
    • electronic Copper Mountain Conference 2000.
    • Henson, V. E., Vassilevski, P.S.: Element-free AMGe: general algorithms for computing interpolation weights in AMG. SIAM J. Sci. Comput. 23, 629-650 (electronic) (2001). Copper Mountain Conference 2000.
    • (2001) SIAM J. Sci. Comput. , vol.23 , pp. 629-650
    • Henson, V.E.1    Vassilevski, P.S.2
  • 15
    • 0036211804 scopus 로고    scopus 로고
    • AMGe based element agglomeration
    • electronic
    • Jones, P. S. V. J. E.: AMGe based element agglomeration. SIAM J. Sci. Comput. 23, 109-133 (electronic) (2001).
    • (2001) SIAM J. Sci. Comput. , vol.23 , pp. 109-133
    • Jones, P.S.V.J.E.1
  • 16
    • 0032634013 scopus 로고    scopus 로고
    • Energy optimization of algebraic multigrid bases
    • Mandel, J., Brezina, M., Vaněk, P.: Energy optimization of algebraic multigrid bases. Computing 62(3), 205-228 (1999).
    • (1999) Computing , vol.62 , Issue.3 , pp. 205-228
    • Mandel, J.1    Brezina, M.2    Vaněk, P.3
  • 17
    • 0000527799 scopus 로고
    • Domain decomposition preconditioning of p-version finite elements with high aspect ratios
    • Mandel, J., Lett, G. S., Domain decomposition preconditioning of p-version finite elements with high aspect ratios. Appl. Num. Math. 8, 411-425 (1991).
    • (1991) Appl. Num. Math. , vol.8 , pp. 411-425
    • Mandel, J.1    Lett, G.S.2
  • 18
  • 19
    • 0001885411 scopus 로고
    • Algebraic multigrid
    • Multigrid methods (S. McCormick, ed.). Philadelphia, PA
    • Ruge, J., Stüben, K.: Algebraic multigrid. In: Multigrid methods (S. McCormick, ed.). SIAM, Philadelphia, PA, 1987.
    • (1987) SIAM
    • Ruge, J.1    Stüben, K.2
  • 21
    • 0347498982 scopus 로고    scopus 로고
    • A review of algebraic multigrid
    • Stüben, K.: A review of algebraic multigrid. GMD Report 69, 1999.
    • (1999) GMD Report , vol.69
    • Stüben, K.1
  • 22
    • 33745644148 scopus 로고    scopus 로고
    • Multigrid. San Diego, CA With contributions by A. Brandt, P. Oswald and K. Stiiben.
    • Trottenberg, U., Oosterlee, C. W., Schuller, A.: Multigrid. San Diego, CA: Academic Press 2001. With contributions by A. Brandt, P. Oswald and K. Stiiben.
    • (2001) Academic Press
    • Trottenberg, U.1    Oosterlee, C.W.2    Schuller, A.3
  • 23
    • 0030388574 scopus 로고    scopus 로고
    • Algebraic multigrid by smoothed aggregation for second- And fourth-order elliptic problems
    • Vanek, P., Mandel, J., Brezina, M.: Algebraic multigrid by smoothed aggregation for second- and fourth-order elliptic problems. Computing 56(3), 179-196 (1996).
    • (1996) Computing , vol.56 , Issue.3 , pp. 179-196
    • Vanek, P.1    Mandel, J.2    Brezina, M.3
  • 24
    • 0041034172 scopus 로고    scopus 로고
    • Convergence of algebraic multigrid based on smoothed aggregation
    • Vanek, P., Brezina, M., Mandel, J.: Convergence of algebraic multigrid based on smoothed aggregation. Numer. Math. 88(3), 559-579 (2001).
    • (2001) Numer. Math. , vol.88 , Issue.3 , pp. 559-579
    • Vanek, P.1    Brezina, M.2    Mandel, J.3
  • 25
    • 0033293066 scopus 로고    scopus 로고
    • An energy-minimizing interpolation for robust multigrid methods
    • Wan, W. L., Chan, T. F., Smith, B.: An energy-minimizing interpolation for robust multigrid methods. SIAM J. Sci. Comput. 21(3), 559-579 (2000).
    • (2000) SIAM J. Sci. Comput. , vol.21 , Issue.3 , pp. 559-579
    • Wan, W.L.1    Chan, T.F.2    Smith, B.3
  • 26
    • 0000570696 scopus 로고
    • Iterative methods by space decomposition and subspace correction
    • Xu, J.: Iterative methods by space decomposition and subspace correction. SIAM Rev. 34, 581-613 (1992).
    • (1992) SIAM Rev. , vol.34 , pp. 581-613
    • Xu, J.1
  • 27
    • 29244478210 scopus 로고    scopus 로고
    • The method of alternating projections and the method of subspace corrections on Hubert space
    • Xu, J., Zikatanov, L.: The method of alternating projections and the method of subspace corrections on Hubert space. J. AMS 15, 1429-1446 (2002).
    • (2002) J. AMS , vol.15 , pp. 1429-1446
    • Xu, J.1    Zikatanov, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.