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Title: Manycore Parallel Computing for a Hybridizable Discontinuous Galerkin Nested Multigrid Method

Abstract

In this work, we present a parallel computing strategy for a hybridizable discontinuous Galerkin (HDG) nested geometric multigrid (GMG) solver. Parallel GMG solvers require a combination of coarse-grain and fine-grain parallelism to improve time-to-solution performance. In this work we focus on fine-grain parallelism. We use Intel's second generation Xeon Phi (Knights Landing) manycore processor. The GMG method achieves ideal convergence rates of 0.2 or less, for high polynomial orders. A matrix free (assembly free) technique is exploited to save considerable memory usage and increase arithmetic intensity. HDG enables static condensation, and due to the discontinuous nature of the discretization, we developed a matrix vector multiply routine that does not require any costly synchronizations or barriers. Our algorithm is able to attain 80% of peak bandwidth performance for higher order polynomials. This is possible due to the data locality inherent in the HDG method. Very high performance is realized for high order schemes, due to good arithmetic intensity, which declines as the order is reduced.

Authors:
 [1];  [2];  [3];  [1]
+ Show Author Affiliations
  1. Rice Univ., Houston, TX (United States). Dept. of Computational and Applied Mathematics
  2. Univ. of Buffalo, Buffalo, NY (United States). Dept. of Computer Science and Engineering
  3. Argonne National Lab. (ANL), Portland, OR (United States). Computer Science and Mathematics Division
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
National Science Foundation (NSF)
OSTI Identifier:
1542582
Grant/Contract Number:  
AC02-06CH11357
Resource Type:
Accepted Manuscript
Journal Name:
SIAM Journal on Scientific Computing
Additional Journal Information:
Journal Volume: 41; Journal Issue: 2; Journal ID: ISSN 1064-8275
Publisher:
SIAM
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; discontinuous Galerkin methods; high performance computing; multigrid; accelerators

Citation Formats

Fabien, Maurice S., Knepley, Matthew G., Mills, Richard T., and Rivière, Béatrice M. Manycore Parallel Computing for a Hybridizable Discontinuous Galerkin Nested Multigrid Method. United States: N. p., 2019. Web. doi:10.1137/17M1128903.
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Fabien, Maurice S., Knepley, Matthew G., Mills, Richard T., & Rivière, Béatrice M. Manycore Parallel Computing for a Hybridizable Discontinuous Galerkin Nested Multigrid Method. United States. https://doi.org/10.1137/17M1128903
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Fabien, Maurice S., Knepley, Matthew G., Mills, Richard T., and Rivière, Béatrice M. Tue . "Manycore Parallel Computing for a Hybridizable Discontinuous Galerkin Nested Multigrid Method". United States. https://doi.org/10.1137/17M1128903. https://www.osti.gov/servlets/purl/1542582.
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@article{osti_1542582,
title = {Manycore Parallel Computing for a Hybridizable Discontinuous Galerkin Nested Multigrid Method},
author = {Fabien, Maurice S. and Knepley, Matthew G. and Mills, Richard T. and Rivière, Béatrice M.},
abstractNote = {In this work, we present a parallel computing strategy for a hybridizable discontinuous Galerkin (HDG) nested geometric multigrid (GMG) solver. Parallel GMG solvers require a combination of coarse-grain and fine-grain parallelism to improve time-to-solution performance. In this work we focus on fine-grain parallelism. We use Intel's second generation Xeon Phi (Knights Landing) manycore processor. The GMG method achieves ideal convergence rates of 0.2 or less, for high polynomial orders. A matrix free (assembly free) technique is exploited to save considerable memory usage and increase arithmetic intensity. HDG enables static condensation, and due to the discontinuous nature of the discretization, we developed a matrix vector multiply routine that does not require any costly synchronizations or barriers. Our algorithm is able to attain 80% of peak bandwidth performance for higher order polynomials. This is possible due to the data locality inherent in the HDG method. Very high performance is realized for high order schemes, due to good arithmetic intensity, which declines as the order is reduced.},
doi = {10.1137/17M1128903},
journal = {SIAM Journal on Scientific Computing},
number = 2,
volume = 41,
place = {United States},
year = {Tue Mar 12 00:00:00 EDT 2019},
month = {Tue Mar 12 00:00:00 EDT 2019}
}
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https://doi.org/10.1137/17M1128903
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Cited by: 11 works
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    Works referencing / citing this record:

    Discontinuous Galerkin approximations in computational mechanics: hybridization, exact geometry and degree adaptivity
    journal, August 2019

    hp-adaptive discontinuous Galerkin solver for elliptic equations in numerical relativity
    journal, October 2019

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