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A practical framework for the construction of prolongation operators for multigrid based on canonical basis functions

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Computing and Visualization in Science

Abstract

We discuss a general framework for the construction of prolongation operators for multigrid methods. It turns out that classical black-box prolongation or prolongation operators based on smoothed aggregation can be classified as special cases. The approach is suitable both for geometric and for purely algebraic multigrid settings. It allows for a simple and efficient implementation and parallelization by introducing canonical basis functions. We show numerical results for several diffusion problems with strongly varying or jumping coefficients. As one possible application for our method we choose three-dimensional medical image segmentation. In addition to that a nonsymmetric convection-diffusion problem is presented.

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Authors and Affiliations

  1. Mathematical Institute, University of Cologne, Weyertal 86-90, 50931, Cologne, Germany

    Roman Wienands

  2. Lehrstuhl Informatik 10 (Systemsimulation), Universität Erlangen-Nuremberg, Cauerstrasse 6, 91058, Erlangen, Germany

    Harald Köstler

Authors
  1. Roman Wienands
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  2. Harald Köstler
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Correspondence to Roman Wienands.

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Communicated by Gabriel Wittum.

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Wienands, R., Köstler, H. A practical framework for the construction of prolongation operators for multigrid based on canonical basis functions. Comput. Visual Sci. 13, 207–220 (2010). https://doi.org/10.1007/s00791-010-0138-0

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  • DOI: https://doi.org/10.1007/s00791-010-0138-0

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