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Coarsening, Sampling, and Smoothing: Elements of the Multilevel Method

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Algorithms for Parallel Processing

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 105))

Abstract

The multilevel method has emerged as one of the most effective methods for solving numerical and combinatorial problems. It has been used in multigrid, domain decomposition, geometric search structures, as well as optimization algorithms for problems such as partitioning and sparse-matrix ordering. This paper presents a systematic treatment of the fundamental elements of the multilevel method. We illustrate, using examples from several fields, the importance and effectiveness of coarsening, sampling, and smoothing (local optimization) in the application of the multilevel method.

Supported in part by an NSF CAREER award (CCR-9502540), an Alfred P. Sloan Research Fellowship, and an Intel research grant.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Shang-Hua Teng

  2. Department of Computer Science, University of Minnesota, Minneapolis, MN, 55455, USA

    Shang-Hua Teng

Authors
  1. Shang-Hua Teng
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Illinois at Urbana, Urbana, IL, 61801-2987, USA

    Michael T. Heath

  2. Department of Computer Science and Engineering, Indian Institute of Technology, Powai, Mumbai, 400076, India

    Abhiram Ranade

  3. Hewlett-Packard, Inc., Palo Alto, CA, 94305-1126, USA

    Robert S. Schreiber

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Teng, SH. (1999). Coarsening, Sampling, and Smoothing: Elements of the Multilevel Method. In: Heath, M.T., Ranade, A., Schreiber, R.S. (eds) Algorithms for Parallel Processing. The IMA Volumes in Mathematics and its Applications, vol 105. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1516-5_11

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  • DOI: https://doi.org/10.1007/978-1-4612-1516-5_11

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7175-8

  • Online ISBN: 978-1-4612-1516-5

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