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Efficient solution of a nonlinear heat conduction problem by use of fast elliptic reduction and multigrid methods

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Book cover Numerical Integration of Differential Equations and Large Linear Systems

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 968))

Abstract

We report on numerical investigations which were made in the development of the code SIHEM (SImulation of HEating processes in Metals). In SIHEM the associated nonlinear parabolic problem (2D-space variables) is treated by a combination of simple (low order) space and implicit time discretizations (Crank-Nicolson) with a time step size control, Newton's or a Newton-like linearization and the use of Fast Elliptic Solvers for the large linear systems. In this report, the emphasis is laid upon systematic investigations and comparisons involving the use of typical Fast Solvers and well-known classical methods. As the solvers are applied at each time and each linearization step the total computing time considerably depends on their efficiency. As a result, we show that the use of a special Multigrid Solver in connection with the time step size control yields a very efficient composite algorithm.

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Authors and Affiliations

  1. Institut für Mathematik der Gesellschaft für Mathematik und Datenverarbeitung (GMD), Schloß Birlinghoven, D-5205, St. Augustin, West Germany

    Karl Solchenbach, Klaus Stüben & Kristian Witsch

  2. Institut für Angewandte Mathematik der Universität Bonn, Wegelerstr. 6, D-5300, Bonn, West Germany

    Ulrich Trottenberg

Authors
  1. Karl Solchenbach
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  2. Klaus Stüben
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  3. Ulrich Trottenberg
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  4. Kristian Witsch
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Juergen Hinze

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© 1982 Springer-Verlag

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Solchenbach, K., Stüben, K., Trottenberg, U., Witsch, K. (1982). Efficient solution of a nonlinear heat conduction problem by use of fast elliptic reduction and multigrid methods. In: Hinze, J. (eds) Numerical Integration of Differential Equations and Large Linear Systems. Lecture Notes in Mathematics, vol 968. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064885

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  • DOI: https://doi.org/10.1007/BFb0064885

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  • Print ISBN: 978-3-540-11970-8

  • Online ISBN: 978-3-540-39374-0

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