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, 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.
- Authors:
-
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Publication Date:
- Research Org.:
- Oak Ridge National Laboratory (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:
- Journal Article: 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. https://doi.org/10.1016/j.jcp.2015.09.008
Hauck, Cory D., Hill, Judith C., and Garrett, C. Kristopher. 2015.
"Optimization and large scale computation of an entropy-based moment closure". United States. https://doi.org/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},
url = {https://www.osti.gov/biblio/1261246},
journal = {Journal of Computational Physics},
issn = {0021-9991},
number = C,
volume = 302,
place = {United States},
year = {Thu Sep 10 00:00:00 EDT 2015},
month = {Thu Sep 10 00:00:00 EDT 2015}
}
Web of Science
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Works referencing / citing this record:
A new entropy-variable-based discretization method for minimum entropy moment approximations of linear kinetic equations
journal, November 2021
- Leibner, Tobias; Ohlberger, Mario
- ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 55, Issue 6
A structure-preserving surrogate model for the closure of the moment system of the Boltzmann equation using convex deep neural networks
text, January 2021
- Schotthöfer, Steffen; Xiao, Tianbai; Frank, Martin
- Karlsruher Institut für Technologie (KIT)