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Filtering algebraic multigrid and adaptive strategies

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Computing and Visualization in Science

Abstract

Solving linear systems arising from partial differential equations, multigrid and multilevel methods have proven optimal complexity and efficiency properties. Due to shortcomings of geometric approaches, algebraic multigrid methods have been developed. One example is the filtering algebraic multigrid method introduced by C. Wagner. This paper proposes a variant of Wagner’s method with substantially improved robustness properties. It is shown, how the class of filtering multigrid methods can be integrated into an adaptive, self-correcting framework. Numerical experiments, which are performed for a class of scaled operators, underline the results.

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Authors and Affiliations

  1. Simulation in Technology, IWR, University of Heidelberg, Im Neuenheimer Feld 368, 69120, Heidelberg, Germany

    Arne Nägel & Gabriel Wittum

  2. Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Box 808, L-561, Livermore, CA, 94551, USA

    Robert D. Falgout

Authors
  1. Arne Nägel
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  2. Robert D. Falgout
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  3. Gabriel Wittum
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Corresponding author

Correspondence to Arne Nägel.

Additional information

Communicated by C. Oosterlee.

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Nägel, A., Falgout, R.D. & Wittum, G. Filtering algebraic multigrid and adaptive strategies. Comput. Visual Sci. 11, 159–167 (2008). https://doi.org/10.1007/s00791-007-0066-9

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  • DOI: https://doi.org/10.1007/s00791-007-0066-9

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