메뉴 건너뛰기




Volumn 21, Issue 3, 1999, Pages 1168-1190

Multigrid for locally refined meshes

Author keywords

[No Author keywords available]

Indexed keywords

ACCELERATION; BOUNDARY CONDITIONS; DIFFUSION; PROBLEM SOLVING; THREE DIMENSIONAL;

EID: 0033296689     PISSN: 10648275     EISSN: None     Source Type: None    
DOI: 10.1137/S1064827597316564     Document Type: Article
Times cited : (3)

References (30)
  • 1
    • 0000014842 scopus 로고
    • The multi-grid method for the diffusion equation with strongly discontinuous coefficients
    • R. E. ALCOUFFE, A. BRANDT, J. E. DENDY, JR., AND J. W. PAINTER, The multi-grid method for the diffusion equation with strongly discontinuous coefficients, SIAM J. Sci. Statist. Comput., 2 (1981), pp. 430-454.
    • (1981) SIAM J. Sci. Statist. Comput. , vol.2 , pp. 430-454
    • Alcouffe, R.E.1    Brandt, A.2    Dendy J.E., Jr.3    Painter, J.W.4
  • 2
    • 84966225317 scopus 로고
    • An optimal order process for solving elliptic finite element equations
    • R. E. BANK AND T. DUPONT, An optimal order process for solving elliptic finite element equations, Math. Comp., 36 (1981), pp. 35-51.
    • (1981) Math. Comp. , vol.36 , pp. 35-51
    • Bank, R.E.1    Dupont, T.2
  • 3
    • 0001377512 scopus 로고
    • The hierarchical basis multigrid method
    • R. E. BANK, T. F. DUPONT, AND H. YSERENTANT, The hierarchical basis multigrid method, Numer. Math., 52 (1988), pp. 427-458.
    • (1988) Numer. Math. , vol.52 , pp. 427-458
    • Bank, R.E.1    Dupont, T.F.2    Yserentant, H.3
  • 4
    • 0343088102 scopus 로고    scopus 로고
    • Hierarchical basis for the convection-diffusion equation on unstructured meshes
    • P. Bjorstad, M. Espedal, and D. Keyes, eds., Wiley and Sons, Sussex, UK
    • R. E. BANK AND S. GUTSCH, Hierarchical basis for the convection-diffusion equation on unstructured meshes, in Ninth International Conference on Domain Decomposition Methods, P. Bjorstad, M. Espedal, and D. Keyes, eds., Wiley and Sons, Sussex, UK, 1997.
    • (1997) Ninth International Conference on Domain Decomposition Methods
    • Bank, R.E.1    Gutsch, S.2
  • 5
    • 0023984323 scopus 로고
    • A preconditioning technique for the efficient solution of problems with local grid refinement
    • J. H. BRAMBLE, R. E. EWING, J. E. PASCIAK, AND A. H. SCHATZ, A preconditioning technique for the efficient solution of problems with local grid refinement, Comput. Methods Appl. Mech. Engrg., 67 (1988), pp. 149-159.
    • (1988) Comput. Methods Appl. Mech. Engrg. , vol.67 , pp. 149-159
    • Bramble, J.H.1    Ewing, R.E.2    Pasciak, J.E.3    Schatz, A.H.4
  • 6
    • 84966238014 scopus 로고
    • The constructuring of preconditioners for elliptic problems on regions partitioned into substructures I
    • J. H. BRAMBLE, J. E. PASCIAK, AND A. H. SCHATZ, The constructuring of preconditioners for elliptic problems on regions partitioned into substructures I, Math. Comp., 46 (1986), pp. 361-369.
    • (1986) Math. Comp. , vol.46 , pp. 361-369
    • Bramble, J.H.1    Pasciak, J.E.2    Schatz, A.H.3
  • 7
    • 84966199070 scopus 로고
    • The constructuring of preconditioners for elliptic problems on regions partitioned into substructures II
    • J. H. BRAMBLE, J. E. PASCIAK, AND A. H. SCHATZ, The constructuring of preconditioners for elliptic problems on regions partitioned into substructures II, Math. Comp., 47 (1986), pp. 103-134.
    • (1986) Math. Comp. , vol.47 , pp. 103-134
    • Bramble, J.H.1    Pasciak, J.E.2    Schatz, A.H.3
  • 8
    • 84966234195 scopus 로고
    • Parallel multilevel preconditioners
    • J. H. BRAMBLE, J. E. PASCIAK, AND J. XU, Parallel multilevel preconditioners, Math. Comp., 55 (1990), pp. 1-22.
    • (1990) Math. Comp. , vol.55 , pp. 1-22
    • Bramble, J.H.1    Pasciak, J.E.2    Xu, J.3
  • 9
    • 0000000860 scopus 로고
    • Guide to multigrid development
    • Multigrid Methods, W. Hackbusch, and U. Trottenberg, eds., Springer-Verlag, Berlin, Heidelberg
    • A. BRANDT, Guide to multigrid development, in Multigrid Methods, W. Hackbusch, and U. Trottenberg, eds., Lecture Notes in Math. 960, Springer-Verlag, Berlin, Heidelberg, 1982.
    • (1982) Lecture Notes in Math. , vol.960
    • Brandt, A.1
  • 10
    • 0001677218 scopus 로고
    • Black box multigrid
    • J. E. DENDY, Black box multigrid, J. Comput. Phys., 48 (1982), pp. 366-386.
    • (1982) J. Comput. Phys. , vol.48 , pp. 366-386
    • Dendy, J.E.1
  • 11
    • 0000555209 scopus 로고
    • Black box multigrid for nonsymmetric problems
    • J. E. DENDY, Black box multigrid for nonsymmetric problems, Appl. Math. Comput., 13 (1983), pp. 261-283.
    • (1983) Appl. Math. Comput. , vol.13 , pp. 261-283
    • Dendy, J.E.1
  • 12
    • 0000025929 scopus 로고
    • Two multigrid methods for three-dimensional problems with discontinuous and anisotropic coefficients
    • J. E. DENDY, JR., Two multigrid methods for three-dimensional problems with discontinuous and anisotropic coefficients, SIAM J. Sci. Statist. Comput., 8 (1987), pp. 673-685.
    • (1987) SIAM J. Sci. Statist. Comput. , vol.8 , pp. 673-685
    • Dendy J.E., Jr.1
  • 13
    • 0024767873 scopus 로고
    • Asynchronous multilevel adaptive methods for solving partial differential equations: Basic ideas
    • L. HART AND S. F. MCCORMICK, Asynchronous multilevel adaptive methods for solving partial differential equations: Basic ideas, Parallel Comput., 12 (1989), pp. 131-144.
    • (1989) Parallel Comput. , vol.12 , pp. 131-144
    • Hart, L.1    Mccormick, S.F.2
  • 14
    • 0040948579 scopus 로고
    • A multigrid method and a combined multigrid-conjugate gradient method for elliptic problems with strongly discontinuous coefficients in general domains
    • KSELP, Rijswijk, the Netherlands
    • R. KETTLER AND J. A. MEIJERINK, A Multigrid Method and a Combined Multigrid-Conjugate Gradient Method for Elliptic Problems with Strongly Discontinuous Coefficients in General Domains, Shell Publ. 604, KSELP, Rijswijk, the Netherlands, 1981.
    • (1981) Shell Publ. , vol.604
    • Kettler, R.1    Meijerink, J.A.2
  • 15
    • 0021478985 scopus 로고
    • Multigrid methods: Convergence theory in a variational framework
    • J.-F. MAITRE AND F. MUSY, Multigrid methods: Convergence theory in a variational framework, SIAM J. Numer. Anal., 21 (1984), pp. 657-671.
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 657-671
    • Maitre, J.-F.1    Musy, F.2
  • 16
    • 0343959849 scopus 로고
    • Algebraic formulation of the multigrid method in the symmetric and positive definite case - A convergence estimation for the V-cycle
    • D. J. Paddon and H. Holstein, eds., Clarendon Press, Oxford, UK
    • J.-F. MAITRE AND F. MUSY, Algebraic formulation of the multigrid method in the symmetric and positive definite case - A convergence estimation for the V-cycle, in Multigrid Methods for Integral and Differential Equations, D. J. Paddon and H. Holstein, eds., Clarendon Press, Oxford, UK, 1985.
    • (1985) Multigrid Methods for Integral and Differential Equations
    • Maitre, J.-F.1    Musy, F.2
  • 17
    • 0024772034 scopus 로고
    • Asynchronous multilevel adaptive methods for solving partial differential equations: Performance results
    • S. F. MCCORMICK AND D. QUINLAN, Asynchronous multilevel adaptive methods for solving partial differential equations: Performance results, Parallel Comput., 12 (1989), pp. 145-156.
    • (1989) Parallel Comput. , vol.12 , pp. 145-156
    • Mccormick, S.F.1    Quinlan, D.2
  • 19
    • 0001721512 scopus 로고
    • Optimal multilevel iterative methods for adaptive grids
    • W. F. MITCHELL, Optimal multilevel iterative methods for adaptive grids, SIAM J. Sci. Statist. Comput., 13 (1992), pp. 146-167.
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , pp. 146-167
    • Mitchell, W.F.1
  • 20
    • 21444442790 scopus 로고    scopus 로고
    • A multigrid method based on incomplete gaussian elimination
    • A. REUSKEN, A multigrid method based on incomplete gaussian elimination, Numer. Linear Algebra Appl., 3 (1996), pp. 369-390.
    • (1996) Numer. Linear Algebra Appl. , vol.3 , pp. 369-390
    • Reusken, A.1
  • 21
    • 0001885411 scopus 로고
    • Algebraic multigrid
    • S. F. McCormick, ed., SIAM, Philadelphia, PA
    • J. W. RUGE AND K. STÜBEN, Algebraic multigrid, in Multigrid Methods, S. F. McCormick, ed., SIAM, Philadelphia, PA, 1987, pp. 73-130.
    • (1987) Multigrid Methods , pp. 73-130
    • Ruge, J.W.1    Stüben, K.2
  • 22
    • 0041400609 scopus 로고    scopus 로고
    • Multigrid techniques for highly indefinite equations
    • N. D. Melson, T. A. Manteuffel, S. F. McCormick, and C. C. Douglas, eds., NASA, Hampton, VA
    • Y. SHAPIRA, Multigrid techniques for highly indefinite equations, in Seventh Copper Mountain Conference on Multigrid Methods, N. D. Melson, T. A. Manteuffel, S. F. McCormick, and C. C. Douglas, eds., Vol. CP 3339, NASA, Hampton, VA, 1996, pp. 689-705.
    • (1996) Seventh Copper Mountain Conference on Multigrid Methods , vol.3339 CP , pp. 689-705
    • Shapira, Y.1
  • 23
    • 0032019318 scopus 로고    scopus 로고
    • Multigrid methods for 3-D definite and indefinite problems
    • Y. SHAPIRA, Multigrid methods for 3-D definite and indefinite problems, Appl. Numer. Math., 26 (1998), pp. 377-398.
    • (1998) Appl. Numer. Math. , vol.26 , pp. 377-398
    • Shapira, Y.1
  • 24
    • 0347599161 scopus 로고    scopus 로고
    • Coloring update methods
    • Y. SHAPIRA, Coloring update methods, BIT, 38 (1998), pp. 180-188.
    • (1998) BIT , vol.38 , pp. 180-188
    • Shapira, Y.1
  • 25
    • 0342653888 scopus 로고    scopus 로고
    • Black-box multigrid solver for definite and indefinite problems
    • O. Axelsson and B. Polman, eds., Katholieke Universiteit Nijmegen, Nijmegen, the Netherlands
    • Y. SHAPIRA, Black-box multigrid solver for definite and indefinite problems, in Algebraic Multi-Level Iteration Methods with Applications, O. Axelsson and B. Polman, eds., Katholieke Universiteit Nijmegen, Nijmegen, the Netherlands, 1996, pp. 235-250.
    • (1996) Algebraic Multi-level Iteration Methods with Applications , pp. 235-250
    • Shapira, Y.1
  • 26
    • 0032388525 scopus 로고    scopus 로고
    • Analysis of matrix-dependent multigrid algorithms
    • Y. SHAPIRA, Analysis of matrix-dependent multigrid algorithms, Numer. Linear Algebra Appl., 5 (1998), pp. 165-201.
    • (1998) Numer. Linear Algebra Appl. , vol.5 , pp. 165-201
    • Shapira, Y.1
  • 27
    • 0343959848 scopus 로고    scopus 로고
    • Algebraic domain decomposition method for unstructured grids
    • P. Bjorstad, M. Espedal, and D. Keyes, eds., Domain Decomposition Press, Bergen, Norway
    • Y. SHAPIRA, Algebraic domain decomposition method for unstructured grids, in Ninth International Conference on Domain Decomposition Methods, P. Bjorstad, M. Espedal, and D. Keyes, eds., Domain Decomposition Press, Bergen, Norway, 1998, pp. 205-214.
    • (1998) Ninth International Conference on Domain Decomposition Methods , pp. 205-214
    • Shapira, Y.1
  • 28
    • 0043018476 scopus 로고    scopus 로고
    • Towards automatic multigrid algorithms for SPD, nonsymmetric and indefinite problems
    • Y. SHAPIRA, M. ISRAELI, AND A. SIDI, Towards automatic Multigrid Algorithms for SPD, nonsymmetric and indefinite problems, SIAM J. Sci. Comput., 17 (1996), pp. 439-453.
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 439-453
    • Shapira, Y.1    Israeli, M.2    Sidi, A.3
  • 29
    • 0002716979 scopus 로고
    • CGS, a fast Lanczos-type solver for nonsymmetric linear systems
    • P. SONNEVELD, CGS, a fast Lanczos-type solver for nonsymmetric linear systems, SIAM J. Sci. Statist. Comput., 10 (1989), pp. 36-52.
    • (1989) SIAM J. Sci. Statist. Comput. , vol.10 , pp. 36-52
    • Sonneveld, P.1
  • 30
    • 0003090969 scopus 로고
    • Matrix-dependent prolongations and restrictions in a blackbox multigrid solver
    • P. M. DE ZEEUW, Matrix-dependent prolongations and restrictions in a blackbox multigrid solver, J. Comput. Appl. Math., 33 (1990), pp. 1-27.
    • (1990) J. Comput. Appl. Math. , vol.33 , pp. 1-27
    • De Zeeuw, P.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.