Cell-based Adaptive Mesh Refinement on the GPU with Applications to Exascale Supercomputing

POSTER

Abstract

We present an OpenCL implementation of a cell-based adaptive mesh refinement (AMR) scheme for the shallow water equations. The challenges associated with ensuring the locality of algorithm architecture to fully exploit the massive number of parallel threads on the GPU is discussed. This includes a proof of concept that a cell-based AMR code can be effectively implemented, even on a small scale, in the memory and threading model provided by OpenCL. Additionally, the program requires dynamic memory in order to properly implement the mesh; as this is not supported in the OpenCL 1.1 standard, a combination of CPU memory management and GPU computation effectively implements a dynamic memory allocation scheme. Load balancing is achieved through a new stencil-based implementation of a space-filling curve, eliminating the need for a complete recalculation of the indexing on the mesh. A cartesian grid hash table scheme to allow fast parallel neighbor accesses is also discussed. Finally, the relative speedup of the GPU-enabled AMR code is compared to the original serial version. We conclude that parallelization using the GPU provides significant speedup for typical numerical applications and is feasible for scientific applications in the next generation of supercomputing.

Authors

  • Dennis Trujillo

    New Mexico State University

  • Young-Yeal Song

    Brigham Young University, Colorado School of Mines, Colorado State University, Yale University, Department of Physics and Astronomy, Brigham Young University, Department of Mechanical Engineering, University of Utah, JILA, NIST and University of Colorado, University of Arizona, MIT, National Institute for Materials Science, Japan, Department of Mechanical Engineering, Brigham Young University, University of New Mexico, Iowa State University, Los Alamos National Lab XCP-2, Utah State University, Weber State University, New Mexico State University, College of Optical Science, University of Arizona, University of Nebraska, Lincoln, J.A. Woollam Co., U.S. Naval Research Laboratory, Arizona State University, BYU Nuclear Physics Group, Brigham Young University Physics and Astronomy, Los Alamos National Laboratory, University of Tsukuba, Japan, Colorado State University, NSF ERC for EUV science and technology, Center for Functional Nanomaterials, Brookhaven National Laboratory, University of Wisconsin, Madison, Utah Valley University, Argonne National Lab

  • Young-Yeal Song

    Brigham Young University, Colorado School of Mines, Colorado State University, Yale University, Department of Physics and Astronomy, Brigham Young University, Department of Mechanical Engineering, University of Utah, JILA, NIST and University of Colorado, University of Arizona, MIT, National Institute for Materials Science, Japan, Department of Mechanical Engineering, Brigham Young University, University of New Mexico, Iowa State University, Los Alamos National Lab XCP-2, Utah State University, Weber State University, New Mexico State University, College of Optical Science, University of Arizona, University of Nebraska, Lincoln, J.A. Woollam Co., U.S. Naval Research Laboratory, Arizona State University, BYU Nuclear Physics Group, Brigham Young University Physics and Astronomy, Los Alamos National Laboratory, University of Tsukuba, Japan, Colorado State University, NSF ERC for EUV science and technology, Center for Functional Nanomaterials, Brookhaven National Laboratory, University of Wisconsin, Madison, Utah Valley University, Argonne National Lab

  • Young-Yeal Song

    Brigham Young University, Colorado School of Mines, Colorado State University, Yale University, Department of Physics and Astronomy, Brigham Young University, Department of Mechanical Engineering, University of Utah, JILA, NIST and University of Colorado, University of Arizona, MIT, National Institute for Materials Science, Japan, Department of Mechanical Engineering, Brigham Young University, University of New Mexico, Iowa State University, Los Alamos National Lab XCP-2, Utah State University, Weber State University, New Mexico State University, College of Optical Science, University of Arizona, University of Nebraska, Lincoln, J.A. Woollam Co., U.S. Naval Research Laboratory, Arizona State University, BYU Nuclear Physics Group, Brigham Young University Physics and Astronomy, Los Alamos National Laboratory, University of Tsukuba, Japan, Colorado State University, NSF ERC for EUV science and technology, Center for Functional Nanomaterials, Brookhaven National Laboratory, University of Wisconsin, Madison, Utah Valley University, Argonne National Lab