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Algebraic Multigrid: From Academia to Industry

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Scientific Computing and Algorithms in Industrial Simulations

Abstract

The research on multigrid in the 1970s opened revolutionary perspectives for the efficient solution of discretized elliptic partial differential equations. In spite of this, it took nearly three decades for it to be seriously recognized and used outside the research community. Surprisingly, not the original geometric multigrid (GMG) but algebraic multigrid (AMG) finally brought the breakthrough. When SCAI (Fraunhofer Institute for Algorithms and Scientific Computing)—formerly an institute of the German National Research Center of Information Technology (GMD)—became a Fraunhofer institute in 2001, applied research at SCAI necessarily got a very strong industrial focus. In particular, the primary goal of SCAI’s further AMG development was to help industrial software developers exploit the scientific progress in numerical solver research to their benefit.

In this report, we will review the development of AMG in general as well as the scientific and non-scientific efforts needed to develop SCAI’s software product SAMG (System Algebraic MultiGrid), today used as solver environment in many industrial simulation tools. The development of SAMG has mostly been driven by requests from industrial partners. We will outline some advanced industrial AMG applications, for instance, in semiconductor design, multi-ion transport and reaction applications, as well as oil reservoir simulation.

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Notes

  1. 1.

    Since AMG by default does not exploit any information about underlying geometric grids, one should actually use the term multilevel rather than multigrid. Nevertheless, multigrid is still used for historical reasons.

  2. 2.

    Computational Dynamics Ltd. was one of the partners in the Europort project.

  3. 3.

    That is, the ratio of the total memory required for all matrices on all levels and the memory required to store the finest-level matrix.

  4. 4.

    To our knowledge, the SMS library is only used in Japan.

  5. 5.

    Which is a result of the requirement of over a 70% return on investment, most of it coming directly through cooperation with industry.

  6. 6.

    We assume the sorting of unknowns at points to be so that the first column of J ij corresponds to pressure derivatives.

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Authors and Affiliations

  1. Fraunhofer Institute for Algorithms and Scientific Computing SCAI, Schloss Birlinghoven, 53757, Sankt Augustin, Germany

    Klaus Stüben, Tanja Clees & Sebastian Gries

  2. University of Colorado at Boulder, Boulder, CO, USA

    John W. Ruge

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  1. Klaus Stüben
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  2. John W. Ruge
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  3. Tanja Clees
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  4. Sebastian Gries
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Correspondence to Klaus Stüben .

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  1. Schloss Birlinghoven, Fraunhofer-Institut SCAI, Sankt Augustin, Germany

    Michael Griebel

  2. Schloss Birlinghoven, Fraunhofer-Institut SCAI, Sankt Augustin, Germany

    Anton Schüller

  3. Schloss Birlinghoven, Fraunhofer-Institut SCAI, Sankt Augustin, Germany

    Marc Alexander Schweitzer

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Stüben, K., Ruge, J.W., Clees, T., Gries, S. (2017). Algebraic Multigrid: From Academia to Industry. In: Griebel, M., Schüller, A., Schweitzer, M. (eds) Scientific Computing and Algorithms in Industrial Simulations. Springer, Cham. https://doi.org/10.1007/978-3-319-62458-7_5

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