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Title: Optimization and large scale computation of an entropy-based moment closure

Abstract

We present computational advances and results in the implementation of an entropy-based moment closure, M N, in the context of linear kinetic equations, with an emphasis on heterogeneous and large-scale computing platforms. Entropy-based closures are known in several cases to yield more accurate results than closures based on standard spectral approximations, such as P N, but the computational cost is generally much higher and often prohibitive. Several optimizations are introduced to improve the performance of entropy-based algorithms over previous implementations. These optimizations include the use of GPU acceleration and the exploitation of the mathematical properties of spherical harmonics, which are used as test functions in the moment formulation. To test the emerging high-performance computing paradigm of communication bound simulations, we present timing results at the largest computational scales currently available. Lastly, these results show, in particular, load balancing issues in scaling the M N algorithm that do not appear for the P N algorithm. We also observe that in weak scaling tests, the ratio in time to solution of M N to P N decreases.

Authors:
 [1];  [2];  [2]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States)
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC)
OSTI Identifier:
1261246
Alternate Identifier(s):
OSTI ID: 1247046
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 302; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; kinetic equations; moment methods; GPU computing; spherical harmonics; high performance computing

Citation Formats

Hauck, Cory D., Hill, Judith C., and Garrett, C. Kristopher. Optimization and large scale computation of an entropy-based moment closure. United States: N. p., 2015. Web. doi:10.1016/j.jcp.2015.09.008.
Hauck, Cory D., Hill, Judith C., & Garrett, C. Kristopher. Optimization and large scale computation of an entropy-based moment closure. United States. doi:10.1016/j.jcp.2015.09.008.
Hauck, Cory D., Hill, Judith C., and Garrett, C. Kristopher. Thu . "Optimization and large scale computation of an entropy-based moment closure". United States. doi:10.1016/j.jcp.2015.09.008. https://www.osti.gov/servlets/purl/1261246.
@article{osti_1261246,
title = {Optimization and large scale computation of an entropy-based moment closure},
author = {Hauck, Cory D. and Hill, Judith C. and Garrett, C. Kristopher},
abstractNote = {We present computational advances and results in the implementation of an entropy-based moment closure, MN, in the context of linear kinetic equations, with an emphasis on heterogeneous and large-scale computing platforms. Entropy-based closures are known in several cases to yield more accurate results than closures based on standard spectral approximations, such as PN, but the computational cost is generally much higher and often prohibitive. Several optimizations are introduced to improve the performance of entropy-based algorithms over previous implementations. These optimizations include the use of GPU acceleration and the exploitation of the mathematical properties of spherical harmonics, which are used as test functions in the moment formulation. To test the emerging high-performance computing paradigm of communication bound simulations, we present timing results at the largest computational scales currently available. Lastly, these results show, in particular, load balancing issues in scaling the MN algorithm that do not appear for the PN algorithm. We also observe that in weak scaling tests, the ratio in time to solution of MN to PN decreases.},
doi = {10.1016/j.jcp.2015.09.008},
journal = {Journal of Computational Physics},
number = C,
volume = 302,
place = {United States},
year = {2015},
month = {9}
}

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