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A Template for Scalable Continuum Dynamic Simulations in Multiple GPUs

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High Performance Computer Applications (ISUM 2015)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 595))

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Abstract

In this work we present a programming philosophy and a template code for achieving computational scalability when using multiple graphics processing units (GPUs) in the numerical solution of any mathematical system of equations found in continuum dynamic simulations. The programming philosophy exploits the principal characteristics of the GPU hardware, with emphasis in the delivering of threads with massive memory fetches, intense calculations using local registers and limited writes to global memory. The philosophy requires explicit formulas for calculations for which domain decomposition is trivial. The domains are decomposed in regions that use the local central processing unit (CPU) to communicate common interfaces using the message passing interface (MPI). A template code for the heat equation is established and tested for scalability. The novelty is that we show a series of codes, constructed from the basic template, that solve all the basic model equations found in continuum dynamics, and present illustrative results. The model equations are the heat equation, the Poisson equation, the shallow-water equations, the flow in porous media equations and the vorticity equations.

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Acknowledgements

This work was partially supported by ABACUS, CONACyT grant EDOMEX-2011-C01-165873.

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Authors and Affiliations

  1. “ABACUS” Centro de Matemáticas Aplicadas y Cómputo de Alto Rendimiento, Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados (CINVESTAV-IPN), Carretera México-Toluca Km 38.5, La Marquesa, 52140, Ocoyoacac, Estado de México, Mexico

    Julián Becerra-Sagredo & Jaime Klapp

  2. Departamento de Física, Facultad de Ciencias, UNAM, Ciudad Universitaria, 04510, Mexico, D.F., Mexico

    Francisco Mandujano & Carlos Málaga

  3. Departamento de Física, Instituto Nacional de Investigaciones Nucleares, La Marquesa Ocoyoacac s/n, Ocoyoacac, Edo. de México, Mexico

    Jaime Klapp

  4. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA

    Irene de Teresa

Authors
  1. Julián Becerra-Sagredo
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  2. Francisco Mandujano
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  3. Carlos Málaga
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  4. Jaime Klapp
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  5. Irene de Teresa
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Corresponding author

Correspondence to Julián Becerra-Sagredo .

Editor information

Editors and Affiliations

  1. ABACUS Centro de Matemáticas Aplicadas, CINVESTAV-IPN, La Marquesa, Mexico

    Isidoro Gitler

  2. Instituto Nacional de Investigaciones Nu, La Marquesa, Mexico

    Jaime Klapp

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Becerra-Sagredo, J., Mandujano, F., Málaga, C., Klapp, J., de Teresa, I. (2016). A Template for Scalable Continuum Dynamic Simulations in Multiple GPUs. In: Gitler, I., Klapp, J. (eds) High Performance Computer Applications. ISUM 2015. Communications in Computer and Information Science, vol 595. Springer, Cham. https://doi.org/10.1007/978-3-319-32243-8_33

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  • DOI: https://doi.org/10.1007/978-3-319-32243-8_33

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32242-1

  • Online ISBN: 978-3-319-32243-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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