{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T18:23:44Z","timestamp":1769019824860,"version":"3.49.0"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,8,24]],"date-time":"2021-08-24T00:00:00Z","timestamp":1629763200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,8,24]],"date-time":"2021-08-24T00:00:00Z","timestamp":1629763200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["RGPAS-2017-507988"],"award-info":[{"award-number":["RGPAS-2017-507988"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["RGPIN-2017-06773"],"award-info":[{"award-number":["RGPIN-2017-06773"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003151","name":"Fonds de Recherche du Qubec - Nature et Technologies","doi-asserted-by":"publisher","award":["New University Researchers start-up"],"award-info":[{"award-number":["New University Researchers start-up"]}],"id":[{"id":"10.13039\/501100003151","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2021,10]]},"DOI":"10.1007\/s10915-021-01620-x","type":"journal-article","created":{"date-parts":[[2021,8,24]],"date-time":"2021-08-24T06:03:38Z","timestamp":1629785018000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Optimal Runge-Kutta Stability Polynomials for Multidimensional High-Order Methods"],"prefix":"10.1007","volume":"89","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0011-5161","authenticated-orcid":false,"given":"Siavash","family":"Hedayati Nasab","sequence":"first","affiliation":[]},{"given":"Carlos A.","family":"Pereira","sequence":"additional","affiliation":[]},{"given":"Brian C.","family":"Vermeire","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,8,24]]},"reference":[{"key":"1620_CR1","doi-asserted-by":"crossref","unstructured":"Huynh, H.T.: A flux reconstruction approach to high-order schemes including discontinuous Galerkin methods. 18th AIAA Computational Fluid Dynamics Conference (2007)","DOI":"10.2514\/6.2007-4079"},{"key":"1620_CR2","volume-title":"Numerical methods for ordinary differential equations","author":"JC Butcher","year":"2002","unstructured":"Butcher, J.C.: Numerical methods for ordinary differential equations. Willy, Hoboken (2002)"},{"key":"1620_CR3","volume-title":"Solving ordinary differential equations I: nonstiff problems","author":"E Hairer","year":"1993","unstructured":"Hairer, E., N\u00f8rsett, S.P., Wanner, G.: Solving ordinary differential equations I: nonstiff problems. Springer, NewYork (1993)"},{"key":"1620_CR4","volume-title":"Solving ordinary differential equations I: stiff and differential-algebraic problems","author":"G Wanner","year":"1996","unstructured":"Wanner, G., Hairer, E.: Solving ordinary differential equations I: stiff and differential-algebraic problems. Springer, NewYork (1996)"},{"key":"1620_CR5","doi-asserted-by":"crossref","unstructured":"Ketcheson, D.I., Ahmadia, A.J.: Optimal stability polynomials for numerical intergration of initial value problems. Commun. Appl. Math. Comput. Sci. 7(2), 247\u2013271 (2012)","DOI":"10.2140\/camcos.2012.7.247"},{"issue":"2","key":"1620_CR6","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1007\/s10915-013-9796-7","volume":"60","author":"EJ Kubatko","year":"2014","unstructured":"Kubatko, E.J., Yeager, B.A., Ketcheson, D.I.: Optimal Strong Stability Preserving Runge-Kutta time discretizations for discontinuous Galerkin methods. J. Sci. Comput. 60(2), 313\u2013344 (2014)","journal-title":"J. Sci. Comput."},{"issue":"10","key":"1620_CR7","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1002\/zamm.19800601005","volume":"60","author":"PJ van Der Houwen","year":"1980","unstructured":"van Der Houwen, P.J., Sommeijer, B.P.: On the internal stability of explicit, m-stage Runge-Kutta methods for large m-values. ZAMM-J. Appl. Math. Mech. 60(10), 479\u2013485 (1980)","journal-title":"ZAMM-J. Appl. Math. Mech."},{"issue":"253","key":"1620_CR8","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1090\/S0025-5718-05-01772-2","volume":"75","author":"SJ Ruuth","year":"2006","unstructured":"Ruuth, S.J.: Global optimization of explicit Strong stability preserving runge-kutta methods. Math. Comput. 75(253), 183\u2013207 (2006)","journal-title":"Math. Comput."},{"issue":"3","key":"1620_CR9","doi-asserted-by":"publisher","first-page":"974","DOI":"10.1137\/S0036142902419284","volume":"42","author":"SJ Ruuth","year":"2004","unstructured":"Ruuth, S.J., Spiteri, R.J.: High-order strong stability preserving Runge-kutta methods with downwind-biased spatial discretizations. SIAM J. Numer. Anal. 42(3), 974\u2013996 (2004)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"1620_CR10","doi-asserted-by":"publisher","first-page":"A957","DOI":"10.1137\/120885899","volume":"35","author":"M Parsani","year":"2013","unstructured":"Parsani, M., Ketcheson, D.I., Deconinck, W.: Optimized explicit Runge-Kutta schemes for the spectral difference method applied to wave propagation problems. SIAM J. Scientific Comput. 35(2), A957\u2013A986 (2013)","journal-title":"SIAM J. Scientific Comput."},{"key":"1620_CR11","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/j.jcp.2019.01.003","volume":"383","author":"BC Vermeire","year":"2019","unstructured":"Vermeire, B.C., Loppi, N.A., Vincent, P.E.: Optimal Runge-Kutta schemes for pseudo time-stepping with high-order unstructured methods. J. Comput. Phys. 383, 55\u201371 (2019)","journal-title":"J. Comput. Phys."},{"key":"1620_CR12","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1016\/j.jcp.2019.05.014","volume":"393","author":"BC Vermeire","year":"2019","unstructured":"Vermeire, B.C.: Paired explicit Runge-Kutta schemes for stiff systems of equations. J. Comput. Phys. 393, 465\u2013483 (2019)","journal-title":"J. Comput. Phys."},{"key":"1620_CR13","doi-asserted-by":"crossref","unstructured":"Vermeire, B.C., Hedayati Nasab, S.: Accelerated implicit-explicit Runge-Kutta schemes for locally stiff systems. J. Comput. Phys. 429, 110022 (2020)","DOI":"10.1016\/j.jcp.2020.110022"},{"issue":"2\u20133","key":"1620_CR14","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1016\/S0168-9274(97)00056-1","volume":"25","author":"UM Ascher","year":"1997","unstructured":"Ascher, U.M., Ruuth, S.J., Spiteri, R.J.: Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations. Appl. Numer. Math. 25(2\u20133), 151\u2013167 (1997)","journal-title":"Appl. Numer. Math."},{"key":"1620_CR15","doi-asserted-by":"crossref","unstructured":"Shoeybi, M., Sv\u00e4rd, M., Ham, F.E., Moin, P.: An adaptive implicit-explicit scheme for the DNS and LES of compressible flows on unstructured grids. J. Comput. Phys. 229(17), 5944\u20135965 (2010)","DOI":"10.1016\/j.jcp.2010.04.027"},{"key":"1620_CR16","doi-asserted-by":"crossref","unstructured":"Hundsdorfer, W., Jaffr\u00e9, J.: Implicit-explicit time stepping with spatial discontinuous finite elements. Appl. Numer. Math. 45(2\u20133), 231\u2013254 (2003)","DOI":"10.1016\/S0168-9274(02)00192-7"},{"key":"1620_CR17","doi-asserted-by":"crossref","unstructured":"Kanevsky, A., Carpenter, M.H., Gottlieb, D., Hesthaven, J.S.: Application of implicit-explicit high-order Runge-Kutta methods to discontinuous Galerkin schemes. J. Comput. Phys. 225(2), 1753\u20131751 (2007)","DOI":"10.1016\/j.jcp.2007.02.021"},{"key":"1620_CR18","doi-asserted-by":"crossref","unstructured":"Vermeire, B.C., Nadarajah, S.: Adaptive IMEX schemes for high-order unstructured methods. J. Comput. Phys. 280, 261\u2013286 (2015)","DOI":"10.1016\/j.jcp.2014.09.016"},{"key":"1620_CR19","unstructured":"Matlab 2016a. Mathworks, 2016"},{"key":"1620_CR20","unstructured":"Grant, M., Boyd, S.: CVX: Matlab software for disciplined convex programming. (2013)"},{"key":"1620_CR21","doi-asserted-by":"crossref","unstructured":"Haga, T., Sawada, K., Wang, Z.J.: An implicit LU-SGS scheme for the spectral volume method on unstructured tetrahedral grids. Comun. Comput. Phys. 6(5), 978 (2009)","DOI":"10.4208\/cicp.2009.v6.p978"},{"issue":"3","key":"1620_CR22","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1051\/mmnp\/20116302","volume":"6","author":"T Haga","year":"2011","unstructured":"Haga, T., Gao, H., Wang, Z.J.: A high-order unifying discontinuous formulation for the Navier-Stokes equations on 3D mixed grids. Math. Model. Nat. Phenom. 6(3), 28\u201359 (2011)","journal-title":"Math. Model. Nat. Phenom."},{"key":"1620_CR23","doi-asserted-by":"publisher","first-page":"695","DOI":"10.1016\/j.jcp.2015.06.020","volume":"298","author":"RC Moura","year":"2015","unstructured":"Moura, R.C., Sherwin, S.J., Peiro, J.: Linear dispersion-diffusion analysis and its application to under-resolved turbulence simulations using discontinuous galerkin spectral\/hp methods. J. Comput. Phys. 298, 695\u2013710 (2015)","journal-title":"J. Comput. Phys."},{"key":"1620_CR24","doi-asserted-by":"crossref","unstructured":"Vincent, P.E., Castonguay, P., Jameson, A.: Insights from Von Neumann Analysis of High-Order flux reconstruction Schemes. J. Comput. Phys. 230(22), 8134\u20138154 (2011)","DOI":"10.1016\/j.jcp.2011.07.013"},{"key":"1620_CR25","unstructured":"Van den Abeele, K.: Development of High-Order Accurate Schemes for Unstructured Grids. Vrije Universiteit Brussel, Belgium (2009). (PhD Thesis at)"},{"issue":"3","key":"1620_CR26","doi-asserted-by":"publisher","first-page":"552","DOI":"10.1007\/s10915-012-9647-y","volume":"55","author":"H Yang","year":"2013","unstructured":"Yang, H., Li, F., Qiu, J.: Dispersion and dissipation errors of two fully discrete discontinuous galerkin methods. J. Scientific Comput. 55(3), 552\u2013574 (2013)","journal-title":"J. Scientific Comput."},{"key":"1620_CR27","doi-asserted-by":"publisher","first-page":"1053","DOI":"10.1016\/j.cma.2016.11.019","volume":"315","author":"BC Vermeire","year":"2017","unstructured":"Vermeire, B.C., Vincent, P.E.: On the behaviour of fully-discrete flux reconstruction schemes. Computer Methods Appl. Mech. Eng. 315, 1053\u20131079 (2017)","journal-title":"Computer Methods Appl. Mech. Eng."},{"key":"1620_CR28","doi-asserted-by":"publisher","first-page":"368","DOI":"10.1016\/j.jcp.2016.09.034","volume":"327","author":"BC Vermeire","year":"2016","unstructured":"Vermeire, B.C., Vincent, P.E.: On the properties of energy stable flux reconstruction schemes for implicit large eddy simulation. J. Comput. Phys. 327, 368\u2013388 (2016)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"1620_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10915-020-01243-8","volume":"83","author":"CA Pereira","year":"2020","unstructured":"Pereira, C.A., Vermeire, B.C.: Fully-discrete analysis of high-order spatial discretizations with optimal explicit runge-kutta methods. J. Scientific Comput. 83(3), 1\u201335 (2020)","journal-title":"J. Scientific Comput."},{"key":"1620_CR30","unstructured":"Castonguay, P.: High-order energy stable flux reconstruction schemes for fluid flow simulations on unstructured grids. Stanford University Press (2012)"},{"issue":"8","key":"1620_CR31","doi-asserted-by":"publisher","first-page":"811","DOI":"10.1002\/fld.3767","volume":"72","author":"ZJ Wang","year":"2013","unstructured":"Wang, Z.J., Fidkowski, K., Abgrall, R., Bassi, F., Caraeni, D., Cary, A., Deconinck, H., Hartmann, R., Hillewaert, K., Huynh, H.T., et al.: High-order CFD methods: current status and perspective. Int. J. Numer. Methods Fluids 72(8), 811\u2013845 (2013)","journal-title":"Int. J. Numer. Methods Fluids"},{"issue":"8","key":"1620_CR32","doi-asserted-by":"publisher","first-page":"2794","DOI":"10.1016\/j.jcp.2010.11.031","volume":"230","author":"WM Van Rees","year":"2011","unstructured":"Van Rees, W.M., Leonard, A., Pullin, D.I., Koumoutsakos, P.: A comparison of vortex and pseudo-spectral methods for the simulation of periodic vortical flows at high reynolds numbers. J. Comput. Phys. 230(8), 2794\u20132805 (2011)","journal-title":"J. Comput. Phys."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-021-01620-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-021-01620-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-021-01620-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,23]],"date-time":"2021-10-23T04:13:55Z","timestamp":1634962435000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-021-01620-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,24]]},"references-count":32,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["1620"],"URL":"https:\/\/doi.org\/10.1007\/s10915-021-01620-x","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,24]]},"assertion":[{"value":"30 August 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 July 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 August 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 August 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 October 2021","order":5,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Update","order":6,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The first and last name order of the author Siavash Hedayati Nasab was corrected.","order":7,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"11"}}