On the arithmetic intensity of high-order finite-volume discretizations for hyperbolic systems of conservation laws
Abstract
It has been conjectured that higher-order discretizations for partial differential equations will have advantages over the lower-order counterparts commonly used today. The reasoning is that the increase in arithmetic operations will be more than offset by the reduction in data transfers and the increase in concurrent floating-point units. To evaluate this conjecture, the arithmetic intensity of a class of high-order finite-volume discretizations for hyperbolic systems of conservation laws is theoretically analyzed for spatial discretizations from orders three through eight in arbitrary dimensions. Additionally, three cache models are considered: the limiting cases of no cache and infinite cache as well as a finite-sized cache model. Models are validated experimentally by measuring floating-point operations and data transfers on an IBM Blue Gene/Q node. Theory and experiments demonstrate that high-order finite-volume methods will be able to provide increases in arithmetic intensity that will be necessary to make better utilization of on-node floating-point capability.
- Authors:
-
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- OSTI Identifier:
- 1860892
- Report Number(s):
- LLNL-JRNL-716535
Journal ID: ISSN 1094-3420; 859004
- Grant/Contract Number:
- AC52-07NA27344
- Resource Type:
- Accepted Manuscript
- Journal Name:
- International Journal of High Performance Computing Applications
- Additional Journal Information:
- Journal Volume: 33; Journal Issue: 1; Journal ID: ISSN 1094-3420
- Publisher:
- SAGE
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; arithmetic intensity; high-order finite-volume methods; hyperbolic systems of conservation laws; processor-memory performance gap; algorithmic balance
Citation Formats
Loffeld, J., and Hittinger, J. A. F. On the arithmetic intensity of high-order finite-volume discretizations for hyperbolic systems of conservation laws. United States: N. p., 2017.
Web. doi:10.1177/1094342017691876.
Loffeld, J., & Hittinger, J. A. F. On the arithmetic intensity of high-order finite-volume discretizations for hyperbolic systems of conservation laws. United States. https://doi.org/10.1177/1094342017691876
Loffeld, J., and Hittinger, J. A. F. Wed .
"On the arithmetic intensity of high-order finite-volume discretizations for hyperbolic systems of conservation laws". United States. https://doi.org/10.1177/1094342017691876. https://www.osti.gov/servlets/purl/1860892.
@article{osti_1860892,
title = {On the arithmetic intensity of high-order finite-volume discretizations for hyperbolic systems of conservation laws},
author = {Loffeld, J. and Hittinger, J. A. F.},
abstractNote = {It has been conjectured that higher-order discretizations for partial differential equations will have advantages over the lower-order counterparts commonly used today. The reasoning is that the increase in arithmetic operations will be more than offset by the reduction in data transfers and the increase in concurrent floating-point units. To evaluate this conjecture, the arithmetic intensity of a class of high-order finite-volume discretizations for hyperbolic systems of conservation laws is theoretically analyzed for spatial discretizations from orders three through eight in arbitrary dimensions. Additionally, three cache models are considered: the limiting cases of no cache and infinite cache as well as a finite-sized cache model. Models are validated experimentally by measuring floating-point operations and data transfers on an IBM Blue Gene/Q node. Theory and experiments demonstrate that high-order finite-volume methods will be able to provide increases in arithmetic intensity that will be necessary to make better utilization of on-node floating-point capability.},
doi = {10.1177/1094342017691876},
journal = {International Journal of High Performance Computing Applications},
number = 1,
volume = 33,
place = {United States},
year = {Wed Feb 01 00:00:00 EST 2017},
month = {Wed Feb 01 00:00:00 EST 2017}
}
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