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An Algebraic Multigrid Method Based on Matching in Graphs

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Domain Decomposition Methods in Science and Engineering XX

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 91))

Abstract

We present an Algebraic Multigrid (AMG) method for graph Laplacian problems. The coarse graphs are constructed recursively by pair-wise aggregation, or matching as in [3] and we use an Algebraic Multilevel Iterations (AMLI) [1, 6] for the solution phase.

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Bibliography

  1. O. Axelsson and P. S. Vassilevski. Algebraic multilevel preconditioning methods. II. SIAM J. Numer. Anal., 27(6):1569–1590, 1990.

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Acknowledgements

The authors gratefully acknowledge the support by the Austrian Academy of Sciences and by the Austrian Science Fund (FWF), Project No. P19170-N18 and the support from the National Science Foundation under grants NSF-DMS 0810982 and NSF-OCI 0749202.

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Authors and Affiliations

  1. Department of Mathematics, The Pennsylvania State University, University Park, PA, 16802, USA

    James Brannick, Yao Chen & Ludmil Zikatanov

  2. Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstraße 69, A-4040, Linz, Austria

    Johannes Kraus

Authors
  1. James Brannick
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  2. Yao Chen
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  3. Johannes Kraus
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  4. Ludmil Zikatanov
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Corresponding author

Correspondence to James Brannick .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Randolph Bank

  2. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Michael Holst

  3. , Courant Institute of Mathematical, New York University, Mercer Street 251, New York, 10012-1185, New York, USA

    Olof Widlund

  4. , Department of Mathematics, Pennsylvania State University, State College, 16802, Pennsylvania, USA

    Jinchao Xu

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Brannick, J., Chen, Y., Kraus, J., Zikatanov, L. (2013). An Algebraic Multigrid Method Based on Matching in Graphs. In: Bank, R., Holst, M., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35275-1_15

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