메뉴 건너뛰기




Volumn 26, Issue 3, 2001, Pages 219-234

Analysis of tensor product multigrid

Author keywords

Anisotropic elliptic problems; Robust multigrid methods; Semi coarsening

Indexed keywords


EID: 0035614659     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1016686408271     Document Type: Article
Times cited : (30)

References (34)
  • 1
    • 38249032508 scopus 로고
    • The Poisson equation on the unit disk: A multigrid solver using polar coordinates
    • S. Barros, The Poisson equation on the unit disk: A multigrid solver using polar coordinates, Appl. Math. Comput. 25 (1988) 123-135.
    • (1988) Appl. Math. Comput. , vol.25 , pp. 123-135
    • Barros, S.1
  • 2
    • 0010534105 scopus 로고
    • Multigrid methods for two- And three-dimensional Poisson-type equations on the sphere
    • S. Barros, Multigrid methods for two- and three-dimensional Poisson-type equations on the sphere, J. Comput. Phys. 92 (1991) 313-348.
    • (1991) J. Comput. Phys. , vol.92 , pp. 313-348
    • Barros, S.1
  • 3
    • 0031074262 scopus 로고    scopus 로고
    • Downwind numbering: Robust multigrid for convection-diffusion problems
    • J. Bey and G. Wittum, Downwind numbering: Robust multigrid for convection-diffusion problems, Appl. Numer. Math. 23 (1997) 177-192.
    • (1997) Appl. Numer. Math. , vol.23 , pp. 177-192
    • Bey, J.1    Wittum, G.2
  • 4
    • 0000671861 scopus 로고
    • A new convergence proof for the multigrid method including the V-cycle
    • D. Braess and W. Hackbusch, A new convergence proof for the multigrid method including the V-cycle, SIAM J. Numer. Anal. 20 (1983) 967-975.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 967-975
    • Braess, D.1    Hackbusch, W.2
  • 5
    • 0004219794 scopus 로고
    • Pitman Research Notes in Mathematics Series, Longman, London
    • J. Bramble, Multigrid Methods, Pitman Research Notes in Mathematics Series, Vol. 294 (Longman, London, 1993).
    • (1993) Multigrid Methods , vol.294
    • Bramble, J.1
  • 6
    • 84966233568 scopus 로고
    • Multi-level adaptive solutions to boundary-value problems
    • A. Brandt, Multi-level adaptive solutions to boundary-value problems, Math. Comp. 31 (1977) 333-390.
    • (1977) Math. Comp. , vol.31 , pp. 333-390
    • Brandt, A.1
  • 8
    • 85011922563 scopus 로고
    • Studies in Mathematics and its Applications, North-Holland, Amsterdam
    • P. Ciarlet, The Finite Element Method for Elliptic Problems, Studies in Mathematics and its Applications, Vol. 4 (North-Holland, Amsterdam, 1978).
    • (1978) The Finite Element Method for Elliptic Problems , vol.4
    • Ciarlet, P.1
  • 9
    • 0040354534 scopus 로고
    • Grandchild of the frequency decomposition multigrid method
    • J. Dendy and C. Tazartes, Grandchild of the frequency decomposition multigrid method, SIAM J. Sci. Comput. 2 (1995) 307-319.
    • (1995) SIAM J. Sci. Comput. , vol.2 , pp. 307-319
    • Dendy, J.1    Tazartes, C.2
  • 10
    • 0003090969 scopus 로고
    • Matrix-dependent prolongations and restrictions in a blackbox multigrid solver
    • P. DeZeeuw, Matrix-dependent prolongations and restrictions in a blackbox multigrid solver, J. Comput. Appl. Math. 33 (1990) 1-27.
    • (1990) J. Comput. Appl. Math. , vol.33 , pp. 1-27
    • Dezeeuw, P.1
  • 11
    • 0031073092 scopus 로고    scopus 로고
    • Additive multilevel preconditioners based on bilinear interpolation, matrix-dependent geometric coarsening and algebraic multigrid coarsening for second-order elliptic PDEs
    • T. Grauschopf, M. Griebel and H. Regler, Additive multilevel preconditioners based on bilinear interpolation, matrix-dependent geometric coarsening and algebraic multigrid coarsening for second-order elliptic PDEs, Appl. Numer. Math. 23 (1997) 63-95.
    • (1997) Appl. Numer. Math. , vol.23 , pp. 63-95
    • Grauschopf, T.1    Griebel, M.2    Regler, H.3
  • 13
    • 34249963996 scopus 로고
    • The frequency decomposition multi-grid method
    • W. Hackbusch, The frequency decomposition multi-grid method, Numer. Math. 56 (1989) 229-245.
    • (1989) Numer. Math. , vol.56 , pp. 229-245
    • Hackbusch, W.1
  • 15
    • 0041590264 scopus 로고
    • The frequency decomposition multi-grid method
    • ed. P. Hemker, Amsterdam, Netherlands, 6-9 July 1993 Birkhäuser, Basel
    • W. Hackbusch, The frequency decomposition multi-grid method, in: Multigrid Methods IV. Proc. of the 4th European Multigrid Conf., ed. P. Hemker, Amsterdam, Netherlands, 6-9 July 1993 (Birkhäuser, Basel, 1994) pp. 43-56.
    • (1994) Multigrid Methods IV. Proc. of the 4th European Multigrid Conf. , pp. 43-56
    • Hackbusch, W.1
  • 16
    • 0031514669 scopus 로고    scopus 로고
    • Downwind Gauss-Seidel smoothing for convection dominated problems
    • W. Hackbusch and T. Probst, Downwind Gauss-Seidel smoothing for convection dominated problems, Numer. Linear Algebra Appl. 4 (1997) 85-102.
    • (1997) Numer. Linear Algebra Appl. , vol.4 , pp. 85-102
    • Hackbusch, W.1    Probst, T.2
  • 19
    • 0002136327 scopus 로고    scopus 로고
    • Directional coarsening and smoothing for anisotropic Navier-Stokes problems
    • D. Mavriplis, Directional coarsening and smoothing for anisotropic Navier-Stokes problems, Electron. Trans. Numer. Anal. 6 (1997) 182-197.
    • (1997) Electron. Trans. Numer. Anal. , vol.6 , pp. 182-197
    • Mavriplis, D.1
  • 20
    • 0001233373 scopus 로고
    • A new multigrid approach to convection problems
    • W. Mulder, A new multigrid approach to convection problems, J. Comput. Phys. 83 (1989) 303-323.
    • (1989) J. Comput. Phys. , vol.83 , pp. 303-323
    • Mulder, W.1
  • 21
    • 0001509694 scopus 로고    scopus 로고
    • Multigrid line smoothers for higher order upwind discretizations of convection dominated problems
    • C. Oosterlee, F. Gaspar, T. Washio and R. Wienands, Multigrid line smoothers for higher order upwind discretizations of convection dominated problems, J. Comput. Phys. 139 (1998) 274-307.
    • (1998) J. Comput. Phys. , vol.139 , pp. 274-307
    • Oosterlee, C.1    Gaspar, F.2    Washio, T.3    Wienands, R.4
  • 22
    • 0004706633 scopus 로고    scopus 로고
    • A robust multilevel algorithm for anisotropic elliptic equations
    • Mathematisches Institut, Universität Würzburg, Würzbug, Germany
    • C. Pflaum, A robust multilevel algorithm for anisotropic elliptic equations, Technical Report 224, Mathematisches Institut, Universität Würzburg, Würzbug, Germany (1998).
    • (1998) Technical Report , vol.224
    • Pflaum, C.1
  • 23
    • 0043093065 scopus 로고    scopus 로고
    • Fast and robust multilevel algorithms
    • Mathematische Institute, Universität Würzburg, Würzburg, Germany
    • C. Pflaum, Fast and robust multilevel algorithms, Habilitationsschrift, Mathematische Institute, Universität Würzburg, Würzburg, Germany (1999).
    • (1999) Habilitationsschrift
    • Pflaum, C.1
  • 24
    • 0030398919 scopus 로고    scopus 로고
    • On a robust multigrid solver
    • A. Reusken, On a robust multigrid solver, Computing 56 (1996) 303-322.
    • (1996) Computing , vol.56 , pp. 303-322
    • Reusken, A.1
  • 25
    • 0001885411 scopus 로고
    • Algebraic multigrid
    • ed. S. McCormick, Frontiers in Applied Mathematics SIAM, Philadelphia, PA, ch. 4
    • J. Ruge and K. Stüben, Algebraic multigrid, in: Multigrid Methods, ed. S. McCormick, Frontiers in Applied Mathematics (SIAM, Philadelphia, PA, 1987) ch. 4, pp. 73-130.
    • (1987) Multigrid Methods , pp. 73-130
    • Ruge, J.1    Stüben, K.2
  • 26
    • 0007452289 scopus 로고
    • New estimates of the contraction number of V-cycle multigrid with applications to anisotropic equations
    • eds. W. Hackbusch and G. Wittum, Notes on Numerical Fluid Mechanics, Vieweg, Braunschweig
    • R. Stevenson, New estimates of the contraction number of V-cycle multigrid with applications to anisotropic equations, in: Incomplete Decompositions, Proc. of the 8th GAMM Seminar, Kiel, eds. W. Hackbusch and G. Wittum, Notes on Numerical Fluid Mechanics, Vol. 41 (Vieweg, Braunschweig, 1993) pp. 159-167.
    • (1993) Incomplete Decompositions, Proc. of the 8th GAMM Seminar, Kiel , vol.41 , pp. 159-167
    • Stevenson, R.1
  • 27
    • 21344485117 scopus 로고
    • Robustness of multi-grid applied to anisotropic equations on convex domains and on domains with re-entrant corners
    • R. Stevenson, Robustness of multi-grid applied to anisotropic equations on convex domains and on domains with re-entrant corners, Numer. Math. 66 (1993) 373-398.
    • (1993) Numer. Math. , vol.66 , pp. 373-398
    • Stevenson, R.1
  • 28
    • 21344476478 scopus 로고
    • Modified ILU as a smoother
    • R. Stevenson, Modified ILU as a smoother, Numer. Math. 68 (1994) 295-309.
    • (1994) Numer. Math. , vol.68 , pp. 295-309
    • Stevenson, R.1
  • 30
    • 0001927802 scopus 로고    scopus 로고
    • Flexible multiple semicoarsening for three-dimensional singularly perturbed problems
    • T. Washio and C. Oosterlee, Flexible multiple semicoarsening for three-dimensional singularly perturbed problems, SIAM J. Sci. Comput. 19 (1998) 1646-1666.
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 1646-1666
    • Washio, T.1    Oosterlee, C.2
  • 32
    • 0000561596 scopus 로고
    • On the robustness of ILU-smoothing
    • G. Wittum, On the robustness of ILU-smoothing, SIAM J. Sci. Statist. Comput. 10 (1989) 699-717.
    • (1989) SIAM J. Sci. Statist. Comput. , vol.10 , pp. 699-717
    • Wittum, G.1
  • 33
    • 0000570696 scopus 로고
    • Iterative methods by space decomposition and subspace correction
    • J. Xu, Iterative methods by space decomposition and subspace correction, SIAM Rev. 34 (1992) 581-613.
    • (1992) SIAM Rev. , vol.34 , pp. 581-613
    • Xu, J.1
  • 34
    • 84971922635 scopus 로고
    • Old and new convergence proofs for multigrid methods
    • H. Yserentant, Old and new convergence proofs for multigrid methods, Acta Numer. (1993) 285-326.
    • (1993) Acta Numer. , pp. 285-326
    • Yserentant, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.