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  • 1995-1999  (5)
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  • 1
    Digitale Medien
    Digitale Medien
    Monotone multigrid methods for elliptic variational inequalities II (1996)
    Springer
    Numerische Mathematik 72 (1996), S. 481-499 
    Details
    ISSN: 0945-3245
    Schlagwort(e): Mathematics Subject Classification (1991): 65N30, 65N55, 35J85
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary. We derive globally convergent multigrid methods for discrete elliptic variational inequalities of the second kind as obtained from the approximation of related continuous problems by piecewise linear finite elements. The coarse grid corrections are computed from certain obstacle problems. The actual constraints are fixed by the preceding nonlinear fine grid smoothing. This new approach allows the implementation as a classical V-cycle and preserves the usual multigrid efficiency. We give $1-O(j^{-3})$ estimates for the asymptotic convergence rates. The numerical results indicate a significant improvement as compared with previous multigrid approaches.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/s002110050178
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  • 2
    Buch
    Buch
    Adaptive monotone multigrid methods for nonlinear variational problems (1997)
    Stuttgart :Teubner,
    Details
    Titel: Adaptive monotone multigrid methods for nonlinear variational problems
    Autor: Kornhuber, Ralf
    Verlag: Stuttgart :Teubner,
    Erscheinungsjahr: 1997
    Seiten: 157 S.
    Serie: Advances in Numerical Mathematics
    Materialart: Buch
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  • 3
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    Monotone Iterations for Elliptic Variational Inequalities (1998)
    Details
    Publikationsdatum: 2014-02-26
    Beschreibung: A wide range of free boundary problems occurring in engineering andindustry can be rewritten as a minimization problem for astrictly convex, piecewise smooth but non--differentiable energy functional.The fast solution of related discretized problemsis a very delicate question, because usual Newton techniquescannot be applied. We propose a new approach based on convex minimization and constrained Newton type linearization. While convex minimization provides global convergence of the overall iteration, the subsequent constrained Newton type linearization is intended to accelerate the convergence speed. We present a general convergence theory and discuss several applications.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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    OPUS
  • 4
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    On Robust Multigrid Methods for Piecewise Smooth Variational Problems (1996)
    Details
    Publikationsdatum: 2014-02-26
    Beschreibung: We consider the fast solution of large, piecewise smooth minimization problems as resulting from the approximation of elliptic free boundary problems. The most delicate question in constructing a multigrid method for a nonlinear, non--smooth problem is how to represent the nonlinearity on the coarse grids. This process usually involves some kind of linearization. The basic idea of monotone multigrid methods to be presented here is first to select a neighborhood of the actual smoothed iterate in which a linearization is possible and then to constrain the coarse grid correction to this neighborhood. Such a local linearization allows to control the local corrections at each coarse grid node in such a way that the energy functional is monotonically decreasing. This approach leads to globally convergent schemes which are robust with respect to local singularities of the given problem. The numerical performance is illustrated by approximating the well-known Barenblatt solution of the porous medium equation.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 5
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    Globally Convergent Multigrid Methods for Porous Medium Type Problems (1997)
    Details
    Publikationsdatum: 2014-02-26
    Beschreibung: We consider the fast solution of large, piecewise smooth minimization problems as typically arising from the finite element discretization of porous media flow. For lack of smoothness, usual Newton multigrid methods cannot be applied. We propose a new approach based on a combination of convex minization with {\em constrained} Newton linearization. No regularization is involved. We show global convergence of the resulting monotone multigrid methods and give logarithmic upper bounds for the asymptotic convergence rates.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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