{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T23:00:52Z","timestamp":1777676452153,"version":"3.51.4"},"reference-count":43,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2010,11,23]],"date-time":"2010-11-23T00:00:00Z","timestamp":1290470400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["The International Journal of High Performance Computing Applications"],"published-print":{"date-parts":[[2011,5]]},"abstract":"<jats:p>We consider the solution of initial value problems (IVPs) of large systems of ordinary differential equations (ODEs) for which memory space requirements determine the choice of the integration method. In particular, we discuss the space-efficient sequential and parallel implementation of embedded Runge\u2014Kutta (RK) methods. Our focus is on the exploitation of a special structure of commonly appearing ODE systems, referred to as \u2018\u2018limited access distance,\u2019\u2019 to improve scalability and memory usage. Such systems may arise, for example, from the semi-discretization of partial differential equations (PDEs).<\/jats:p>\n                  <jats:p>The storage space required by classical RK methods is directly proportional to the dimension n of the ODE system and the number of stages s of the method. We propose an implementation strategy based on a pipelined processing of the stages of the RK method and show how the memory usage of this computation scheme can be reduced to less than three storage registers by an overlapping of vectors without compromising the choice of method coefficients or the potential for efficient stepsize control. We analyze and compare the scalability of different parallel implementation strategies in detailed runtime experiments on different modern parallel architectures.<\/jats:p>","DOI":"10.1177\/1094342010384418","type":"journal-article","created":{"date-parts":[[2010,11,23]],"date-time":"2010-11-23T20:49:31Z","timestamp":1290545371000},"page":"236-255","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":7,"title":["Parallel Low-Storage Runge\u2014Kutta Solvers for ODE Systems with Limited Access Distance"],"prefix":"10.1177","volume":"25","author":[{"given":"Matthias","family":"Korch","sequence":"first","affiliation":[{"name":"University of Bayreuth, Department of Computer Science, Germany,"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thomas","family":"Rauber","sequence":"additional","affiliation":[{"name":"University of Bayreuth, Department of Computer Science, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2010,11,23]]},"reference":[{"key":"atypb1","volume-title":"Optimizing Compilers for Modern Architectures: A Dependence Based Approach","author":"Allen, R.","year":"2002"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-03869-3_72"},{"key":"atypb3","author":"Baskaran, M.M.","year":"2010","journal-title":"IEEE\/ACM International Symposium on Code Generation and Optimization (CGO)"},{"key":"atypb4","volume-title":"10th AIAA\/CEAS Aeroacoustics Conference","author":"Berland, J."},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/j.compfluid.2005.04.003"},{"key":"atypb6","volume-title":"11th ACM Int. Conf. on Supercomputing","author":"Bilmes, J."},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1145\/567806.567807"},{"key":"atypb8","volume":"92","author":"Brankin, R.W.","year":"1992","journal-title":"Softreport"},{"key":"atypb9","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198534327.001.0001","volume-title":"Parallel and Sequential Methods for Ordinary Differential Equations","author":"Burrage, K.","year":"1995"},{"key":"atypb10","volume-title":"Programming with POSIX Threads","author":"Butenhof, D.R.","year":"1997"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2004.05.012"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2007.10.003"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1137\/1027140"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/0771-050X(80)90013-3"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/S0927-5452(98)80066-X"},{"issue":"2","key":"atypb16","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/BF02234758","volume":"4","author":"Fehlberg, E.","year":"1969","journal-title":"Computing"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/0168-9274(93)90039-T"},{"key":"atypb18","volume-title":"Solving Ordinary Differential Equations I: Nonstiff Problems","author":"Hairer, E.","year":"2000","edition":"2"},{"key":"atypb19","volume":"100","author":"Hull, T.E.","year":"1976","journal-title":"Technical Report"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/0732002"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(95)00219-7"},{"key":"atypb22","volume":"109111","author":"Kennedy, C.A.","year":"1994","journal-title":"Technical Report NASA"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-9274(99)00141-5"},{"key":"atypb24","volume-title":"Effiziente Implementierung eingebetteter Runge-Kutta-Verfahren durch Ausnutzung der Speicherzugriffslokalit\u00e4t. Doctoral thesis","author":"Korch, M.","year":"2006"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-45209-6_113"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpdc.2005.09.003"},{"key":"atypb27","volume":"1","author":"Korch, M.","year":"2010","journal-title":"Bayreuth Reports on Parallel and Distributed Systems"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.1982.1270004"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2007.02.004"},{"key":"atypb30","doi-asserted-by":"crossref","unstructured":"N\u00f8rsett, S.P. and Simonsen, H.H. ( 1989). Aspects of parallel Runge-Kutta methods. In Numerical Methods for Ordinary Differential Equations. Number 1386 in LNM, pp. 103-117.","DOI":"10.1007\/BFb0089234"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1016\/0771-050X(81)90010-3"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1096-9128(199906)11:7<367::AID-CPE430>3.0.CO;2-G"},{"issue":"3","key":"atypb33","first-page":"133","volume":"12","author":"Rauber, T.","year":"2004","journal-title":"Sci. Prog"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-05-01772-2"},{"key":"atypb35","volume-title":"The Numerical Method of Lines","author":"Schiesser, W.E.","year":"1991"},{"key":"atypb36","volume-title":"MPI the complete reference","author":"Snir, M.","year":"1998","edition":"2"},{"key":"atypb37","volume-title":"Numerik gew\u00f6hnlicher Differentialgleichungen","author":"Strehmel, K.","year":"1995"},{"key":"atypb38","author":"Tiwari, A.","year":"2009","journal-title":"International Parallel and Distributed Processing Symposium (IPDPS)"},{"key":"atypb39","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(90)90200-J"},{"key":"atypb40","doi-asserted-by":"publisher","DOI":"10.2528\/PIERL09042305"},{"key":"atypb41","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8191(00)00087-9"},{"key":"atypb42","first-page":"95","volume":"2","author":"White, J.","year":"1985","journal-title":"Trans. of the Soc. for Computer Simulation"},{"key":"atypb43","volume-title":"High Performance Compilers for Parallel Computing","author":"Wolfe, M.","year":"1996"}],"container-title":["The International Journal of High Performance Computing Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1094342010384418","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1094342010384418","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T08:18:58Z","timestamp":1777450738000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/1094342010384418"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,11,23]]},"references-count":43,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2011,5]]}},"alternative-id":["10.1177\/1094342010384418"],"URL":"https:\/\/doi.org\/10.1177\/1094342010384418","relation":{},"ISSN":["1094-3420","1741-2846"],"issn-type":[{"value":"1094-3420","type":"print"},{"value":"1741-2846","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,11,23]]}}}