Efficiency of High Order Spectral Element Methods on Petascale Architectures

Handle URI:
http://hdl.handle.net/10754/622140
Title:
Efficiency of High Order Spectral Element Methods on Petascale Architectures
Authors:
Hutchinson, Maxwell; Heinecke, Alexander; Pabst, Hans; Henry, Greg; Parsani, Matteo ( 0000-0001-7300-1280 ) ; Keyes, David E. ( 0000-0002-4052-7224 )
Abstract:
High order methods for the solution of PDEs expose a tradeoff between computational cost and accuracy on a per degree of freedom basis. In many cases, the cost increases due to higher arithmetic intensity while affecting data movement minimally. As architectures tend towards wider vector instructions and expect higher arithmetic intensities, the best order for a particular simulation may change. This study highlights preferred orders by identifying the high order efficiency frontier of the spectral element method implemented in Nek5000 and NekBox: the set of orders and meshes that minimize computational cost at fixed accuracy. First, we extract Nek’s order-dependent computational kernels and demonstrate exceptional hardware utilization by hardware-aware implementations. Then, we perform productionscale calculations of the nonlinear single mode Rayleigh-Taylor instability on BlueGene/Q and Cray XC40-based supercomputers to highlight the influence of the architecture. Accuracy is defined with respect to physical observables, and computational costs are measured by the corehour charge of the entire application. The total number of grid points needed to achieve a given accuracy is reduced by increasing the polynomial order. On the XC40 and BlueGene/Q, polynomial orders as high as 31 and 15 come at no marginal cost per timestep, respectively. Taken together, these observations lead to a strong preference for high order discretizations that use fewer degrees of freedom. From a performance point of view, we demonstrate up to 60% full application bandwidth utilization at scale and achieve ≈1PFlop/s of compute performance in Nek’s most flop-intense methods.
KAUST Department:
Extreme Computing Research Center
Citation:
Hutchinson M, Heinecke A, Pabst H, Henry G, Parsani M, et al. (2016) Efficiency of High Order Spectral Element Methods on Petascale Architectures. High Performance Computing: 449–466. Available: http://dx.doi.org/10.1007/978-3-319-41321-1_23.
Publisher:
Springer Nature
Journal:
Lecture Notes in Computer Science
Conference/Event name:
31st International Conference on High Performance Computing, ISC High Performance 2016
Issue Date:
14-Jun-2016
DOI:
10.1007/978-3-319-41321-1_23
Type:
Conference Paper
ISSN:
0302-9743; 1611-3349
Appears in Collections:
Conference Papers; Extreme Computing Research Center

Full metadata record

DC FieldValue Language
dc.contributor.authorHutchinson, Maxwellen
dc.contributor.authorHeinecke, Alexanderen
dc.contributor.authorPabst, Hansen
dc.contributor.authorHenry, Gregen
dc.contributor.authorParsani, Matteoen
dc.contributor.authorKeyes, David E.en
dc.date.accessioned2017-01-02T08:10:21Z-
dc.date.available2017-01-02T08:10:21Z-
dc.date.issued2016-06-14en
dc.identifier.citationHutchinson M, Heinecke A, Pabst H, Henry G, Parsani M, et al. (2016) Efficiency of High Order Spectral Element Methods on Petascale Architectures. High Performance Computing: 449–466. Available: http://dx.doi.org/10.1007/978-3-319-41321-1_23.en
dc.identifier.issn0302-9743en
dc.identifier.issn1611-3349en
dc.identifier.doi10.1007/978-3-319-41321-1_23en
dc.identifier.urihttp://hdl.handle.net/10754/622140-
dc.description.abstractHigh order methods for the solution of PDEs expose a tradeoff between computational cost and accuracy on a per degree of freedom basis. In many cases, the cost increases due to higher arithmetic intensity while affecting data movement minimally. As architectures tend towards wider vector instructions and expect higher arithmetic intensities, the best order for a particular simulation may change. This study highlights preferred orders by identifying the high order efficiency frontier of the spectral element method implemented in Nek5000 and NekBox: the set of orders and meshes that minimize computational cost at fixed accuracy. First, we extract Nek’s order-dependent computational kernels and demonstrate exceptional hardware utilization by hardware-aware implementations. Then, we perform productionscale calculations of the nonlinear single mode Rayleigh-Taylor instability on BlueGene/Q and Cray XC40-based supercomputers to highlight the influence of the architecture. Accuracy is defined with respect to physical observables, and computational costs are measured by the corehour charge of the entire application. The total number of grid points needed to achieve a given accuracy is reduced by increasing the polynomial order. On the XC40 and BlueGene/Q, polynomial orders as high as 31 and 15 come at no marginal cost per timestep, respectively. Taken together, these observations lead to a strong preference for high order discretizations that use fewer degrees of freedom. From a performance point of view, we demonstrate up to 60% full application bandwidth utilization at scale and achieve ≈1PFlop/s of compute performance in Nek’s most flop-intense methods.en
dc.publisherSpringer Natureen
dc.subjectHigh orderen
dc.subjectNek5000en
dc.subjectSpectral element methoden
dc.subjectVectorizationen
dc.titleEfficiency of High Order Spectral Element Methods on Petascale Architecturesen
dc.typeConference Paperen
dc.contributor.departmentExtreme Computing Research Centeren
dc.identifier.journalLecture Notes in Computer Scienceen
dc.conference.date2016-06-19 to 2016-06-23en
dc.conference.name31st International Conference on High Performance Computing, ISC High Performance 2016en
dc.conference.locationFrankfurt, DEUen
dc.contributor.institutionDepartment of Physics, University of Chicago, Chicago, IL, United Statesen
dc.contributor.institutionIntel Corporation, Santa Clara, CA, United Statesen
dc.contributor.institutionIntel Semiconductor AG, Zurich, Switzerlanden
dc.contributor.institutionIntel Corporation, Hillsboro, OR, United Statesen
kaust.authorParsani, Matteoen
kaust.authorKeyes, David E.en
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