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Optimizing the performance of the spectral/hp element method with collective linear algebra operations

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Title: Optimizing the performance of the spectral/hp element method with collective linear algebra operations
Authors: Moxey, D
Cantwell, C
Kirby, RM
Sherwin, S
Item Type: Journal Article
Abstract: As computing hardware evolves, increasing core counts mean that memory bandwidth is becoming the deciding factor in attaining peak performance of numerical methods. High-order finite element methods, such as those implemented in the spectral/hp framework Nektar++, are particularly well-suited to this environment. Unlike low-order methods that typically utilize sparse storage, matrices representing high-order operators have greater density and richer structure. In this paper, we show how these qualities can be exploited to increase runtime performance on nodes that comprise a typical high-performance computing system, by amalgamating the action of key operators on multiple elements into a single, memorye!cient block. We investigate di↵erent strategies for achieving optimal performance across a range of polynomial orders and element types. As these strategies all depend on external factors such as BLAS implementation and the geometry of interest, we present a technique for automatically selecting the most e!cient strategy at runtime.
Issue Date: 29-Jul-2016
Date of Acceptance: 1-Jul-2016
URI: http://hdl.handle.net/10044/1/37414
DOI: https://dx.doi.org/10.1016/j.cma.2016.07.001
ISSN: 0045-7825
Publisher: Elsevier
Start Page: 628
End Page: 645
Journal / Book Title: Computer Methods in Applied Mechanics and Engineering
Volume: 310
Copyright Statement: © 2016 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons. org/licenses/by/4.0/).
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (E
McLaren Racing Limited
Royal Academy Of Engineering
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (E
Engineering & Physical Science Research Council (E
Funder's Grant Number: EP/H000208/1
EP/I037946/1
AEDZ_P42726
AEDZ_P40009
EP/K038788/1
EP/K037536/1
EP/L000407/1
Keywords: Applied Mathematics
01 Mathematical Sciences
09 Engineering
Publication Status: Published
Appears in Collections:Faculty of Engineering
Aeronautics



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