{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T23:45:08Z","timestamp":1783035908897,"version":"3.54.6"},"reference-count":20,"publisher":"SAGE Publications","issue":"5","license":[{"start":{"date-parts":[[2020,6,15]],"date-time":"2020-06-15T00:00:00Z","timestamp":1592179200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["The International Journal of High Performance Computing Applications"],"published-print":{"date-parts":[[2020,9]]},"abstract":"<jats:p>Performance tests and analyses are critical to effective high-performance computing software development and are central components in the design and implementation of computational algorithms for achieving faster simulations on existing and future computing architectures for large-scale application problems. In this article, we explore performance and space-time trade-offs for important compute-intensive kernels of large-scale numerical solvers for partial differential equations (PDEs) that govern a wide range of physical applications. We consider a sequence of PDE-motivated bake-off problems designed to establish best practices for efficient high-order simulations across a variety of codes and platforms. We measure peak performance (degrees of freedom per second) on a fixed number of nodes and identify effective code optimization strategies for each architecture. In addition to peak performance, we identify the minimum time to solution at 80% parallel efficiency. The performance analysis is based on spectral and p-type finite elements but is equally applicable to a broad spectrum of numerical PDE discretizations, including finite difference, finite volume, and h-type finite elements.<\/jats:p>","DOI":"10.1177\/1094342020915762","type":"journal-article","created":{"date-parts":[[2020,6,15]],"date-time":"2020-06-15T03:22:12Z","timestamp":1592191332000},"page":"562-586","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":64,"title":["Scalability of high-performance PDE solvers"],"prefix":"10.1177","volume":"34","author":[{"given":"Paul","family":"Fischer","sequence":"first","affiliation":[{"name":"Mathematics and Computer Science, Argonne National Laboratory, Lemont, IL, USA"},{"name":"Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL, USA"},{"name":"Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5646-5689","authenticated-orcid":false,"given":"Misun","family":"Min","sequence":"additional","affiliation":[{"name":"Mathematics and Computer Science, Argonne National Laboratory, Lemont, IL, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thilina","family":"Rathnayake","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Som","family":"Dutta","sequence":"additional","affiliation":[{"name":"Mechanical and Aerospace Engineering, Utah State University, Logan, UT, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tzanio","family":"Kolev","sequence":"additional","affiliation":[{"name":"Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Veselin","family":"Dobrev","sequence":"additional","affiliation":[{"name":"Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jean-Sylvain","family":"Camier","sequence":"additional","affiliation":[{"name":"Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martin","family":"Kronbichler","sequence":"additional","affiliation":[{"name":"Institute for Computational Mechanics, Technical University of Munich, Garching, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tim","family":"Warburton","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Virginia Tech, Blacksburg, VA, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kasia","family":"\u015awirydowicz","sequence":"additional","affiliation":[{"name":"National Renewable Energy Laboratory, Lakewood, CO, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jed","family":"Brown","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Colorado, Boulder, CO, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2020,6,15]]},"reference":[{"key":"bibr1-1094342020915762","doi-asserted-by":"publisher","DOI":"10.1515\/jnma-2017-0058"},{"key":"bibr2-1094342020915762","doi-asserted-by":"publisher","DOI":"10.1137\/18M1194997"},{"key":"bibr4-1094342020915762","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511546792"},{"key":"bibr5-1094342020915762","unstructured":"Fischer P (1989) Spectral element solution of the Navier-Stokes equations on high performance distributed-memory parallel processors. 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