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Parallel Comput."],"published-print":{"date-parts":[[2021,9,30]]},"abstract":"<jats:p>\n            We discuss the efficient implementation of a high-performance second-order collocation-type finite-element scheme for solving the compressible Euler equations of gas dynamics on unstructured meshes. The solver is based on the\n            <jats:italic>convex-limiting<\/jats:italic>\n            technique introduced by Guermond et\u00a0al.\u00a0(SIAM J. Sci. Comput. 40, A3211\u2013A3239, 2018). As such, it is\n            <jats:italic>invariant-domain preserving<\/jats:italic>\n            ; i.e., the solver maintains important physical invariants and is guaranteed to be stable without the use of ad hoc tuning parameters. This stability comes at the expense of a significantly more involved algorithmic structure that renders conventional high-performance discretizations challenging. We develop an algorithmic design that allows SIMD vectorization of the compute kernel, identify the main ingredients for a good node-level performance, and report excellent weak and strong scaling of a hybrid thread\/MPI parallelization.\n          <\/jats:p>","DOI":"10.1145\/3470637","type":"journal-article","created":{"date-parts":[[2021,9,20]],"date-time":"2021-09-20T18:27:58Z","timestamp":1632162478000},"page":"1-30","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":23,"title":["Efficient Parallel 3D Computation of the Compressible Euler Equations with an Invariant-domain Preserving Second-order Finite-element Scheme"],"prefix":"10.1145","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4960-5217","authenticated-orcid":false,"given":"Matthias","family":"Maier","sequence":"first","affiliation":[{"name":"Department of Mathematics, Texas A&amp;M University, TX, USA"}]},{"given":"Martin","family":"Kronbichler","sequence":"additional","affiliation":[{"name":"Institute for Computational Mechanics, Technical University of Munich, Boltzmannstrasse, Garching, Germany"}]}],"member":"320","published-online":{"date-parts":[[2021,9,20]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/3380930"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1515\/jnma-2019-0064"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2020.02.022"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-47956-5_8"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2016.07.001"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1137\/17M1148384"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1109\/MCSE.2006.102"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1177\/1094342005054257"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(89)90183-6"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/800195.805928"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpdc.2014.07.003"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1177\/1094342020915762"},{"key":"e_1_2_1_13_1","unstructured":"Agner Fog. 2020. VCL\u2014C++ Vector Class Library Manual. Technical Report. Retrieved from https:\/\/github.com\/vectorclass\/version2\/releases\/download\/v2.01.02\/vcl_manual.pdf.  Agner Fog. 2020. VCL\u2014C++ Vector Class Library Manual. Technical Report. Retrieved from https:\/\/github.com\/vectorclass\/version2\/releases\/download\/v2.01.02\/vcl_manual.pdf."},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1137\/17M1149961"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1137\/130950240"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2010.11.043"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1137\/120903312"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2016.05.054"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1137\/16M1074291"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1137\/16M1106560"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.5555\/1855048"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(83)90118-3"},{"key":"e_1_2_1_23_1","unstructured":"Jared Hoberock. 2019. Working Draft C ++ Extensions for Parallelism Version 2. Technical Report.  Jared Hoberock. 2019. Working Draft C ++ Extensions for Parallelism Version 2. Technical Report."},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1137\/130930352"},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.compfluid.2012.04.012"},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/3325864"},{"key":"e_1_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.1137\/16M110455X"},{"key":"e_1_2_1_29_1","volume-title":"Algebraic Flux Correction II. Compressible Euler Equations","author":"Kuzmin Dmitri","unstructured":"Dmitri Kuzmin and Matthias M\u00f6ller . 2005. Algebraic Flux Correction II. Compressible Euler Equations . Springer , 207\u2013250. DOI:https:\/\/doi.org\/10.1007\/3-540-27206-2_7 10.1007\/3-540-27206-2_7 Dmitri Kuzmin and Matthias M\u00f6ller. 2005. Algebraic Flux Correction II. Compressible Euler Equations. Springer, 207\u2013250. 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