{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:33:40Z","timestamp":1787337220687,"version":"build-2736575974"},"reference-count":18,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>Frequently, the computation of derivatives for optimizing time-dependent problems is based on the integration of the adjoint differential equation. For this purpose, the knowledge of the complete forward solution may be required. Similar information is needed in the context of a posteriori error estimation with respect to a given functional. In the area of flow control, especially for three dimensional problems, it is usually impossible to keep track of the full forward solution due to the lack of storage capacities. Further, for many problems, adaptive time-stepping procedures are needed toward efficient integration schemes in time. Therefore, standard optimal offline checkpointing strategies are usually not well suited in that framework. In this paper we present two algorithms for an online checkpointing procedure that determines the checkpoint distribution on the fly. We prove that these approaches yield checkpointing distributions that are either optimal or almost optimal with only a small gap to optimality. Numerical results underline the theoretical results.<\/jats:p>","DOI":"10.1137\/080742439","type":"journal-article","created":{"date-parts":[[2010,3,10]],"date-time":"2010-03-10T18:14:29Z","timestamp":1268244869000},"page":"836-854","source":"Crossref","is-referenced-by-count":40,"title":["New Algorithms for Optimal Online Checkpointing"],"prefix":"10.1137","volume":"32","author":[{"given":"Philipp","family":"Stumm","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrea","family":"Walther","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,3,10]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1080\/10556780701228532"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492901000010"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"B. Cockburn, C. Johnson, C.W. Chu, and E. Tedmor,\n                      Advanced Numerical Approximation of Nonlinear Hyperbolic Equations\n                      , Springer, New York, 1998.","DOI":"10.1007\/BFb0096351"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1145\/347837.347846"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"A. Griewank and A. Walther.\n                      Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation\n                      , 2nd ed., SIAM, Philadelphia, 2008.","DOI":"10.1137\/1.9780898717761"},{"key":"R6","doi-asserted-by":"crossref","unstructured":"M. D. Gunzburger,\n                      Perspectives in Flow Control and Optimization\n                      , Adv. Des. Control 5, SIAM, Philadelphia, 2002.","DOI":"10.1137\/1.9780898718720"},{"key":"R7","unstructured":"E. Hairer, S. P. Norsett, and G. Wanner,\n                      Solving Ordinary Differential Equations\n                      I, Springer, New York, 1993."},{"key":"R8","doi-asserted-by":"crossref","unstructured":"V. Heuveline and A. Walther,\n                      Online checkpointing for parallel adjoint computation in PDEs: Application to goal-oriented adaptivity and flow control\n                      , in Euro-Par 2006 Parallel Processing, W. E. Nagel, W. V. Walter, and W. Lehner, eds., Springer, New York, 2006, pp. 689\u2013699.","DOI":"10.1007\/11823285_72"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012999361810"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1080\/10556780410001684158"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1080\/10556789808805717"},{"key":"R12","unstructured":"M. Maier and U. Naumann,\n                      Intraprocedural adjoint code generated by the differentiation-enabled NAGWare Fortran compiler\n                      , in Proceedings of the 5th International Conference on Engineering Computational Technology (ECT 2006), Civil-Comp Press, Stirling, UK, 2006, pp. 1\u201319."},{"key":"R13","doi-asserted-by":"crossref","unstructured":"U. Naumann and J. Riehme,\n                      Computing adjoints with the NAGWare Fortran $95$ compiler\n                      , in Automatic Differentiation: Applications, Theory, and Tools, H. B\u00fccker, G. Corliss, P. Hovland, U. Naumann, and B. Norris, eds., Lect. Notes Comput. Sci. Eng. 50, Springer, Berlin, 2005, pp. 159\u2013170.","DOI":"10.1007\/3-540-28438-9_14"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1145\/1114268.1114270"},{"key":"R15","doi-asserted-by":"crossref","unstructured":"U. Naumann, J. Riehme, J. Stiller, and A. Walther,\n                      Adjoints for time-dependent optimal control\n                      , in Advances in Automatic Differentiation, C. Bischof, M. B\u00fccker, P. Hovland, U. Naumann, and J. Utke, eds., Lect. Notes Comput. Sci. Eng. 64, Berlin, Springer, 2008, pp. 175\u2013185.","DOI":"10.1007\/978-3-540-68942-3_16"},{"key":"R16","unstructured":"R. Serban and A. C. Hindmarsh,\n                      CVODES: An ODE Solver with Sensitivity Analysis Capabilities\n                      , Tech. report UCRL-JP-20039, Lawrence Livermore National Laboratory, Livermore, CA, 2003."},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1137\/080718036"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1137\/080727890"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/080742439","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:50:20Z","timestamp":1787334620000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/080742439"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":18,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/080742439"],"URL":"https:\/\/doi.org\/10.1137\/080742439","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}