{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,20]],"date-time":"2026-09-20T11:38:23Z","timestamp":1789904303957,"version":"4.0.1"},"reference-count":48,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"name":"CST Computer Simulation Technology AG"},{"DOI":"10.13039\/501100002347","name":"Bundesministerium f\u00fcr Bildung und Forschung","doi-asserted-by":"publisher","award":["05M13PMA"],"award-info":[{"award-number":["05M13PMA"]}],"id":[{"id":"10.13039\/501100002347","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>Engineers manually optimizing a structure using finite element based simulation software often employ an iterative approach where in each iteration they change the structure slightly and resimulate. Standard finite element based simulation software is usually not well suited for this workflow, as it restarts in each iteration, even for tiny changes. In settings with complex local microstructure, where a fine mesh is required to capture the geometric detail, localized model reduction can improve this workflow. To this end, we introduce ArbiLoMod, a method which allows fast recomputation after arbitrary local modifications. It employs a domain decomposition and a localized form of the reduced basis method for model order reduction. It assumes that the reduced basis on many of the unchanged domains can be reused after a localized change. The reduced model is adapted when necessary, steered by a localized error indicator. The global error introduced by the model order reduction is controlled by a robust and efficient localized a posteriori error estimator, certifying the quality of the result. We demonstrate ArbiLoMod for a coercive, parameterized example with changing structure.<\/jats:p>","DOI":"10.1137\/15m1054213","type":"journal-article","created":{"date-parts":[[2017,8,17]],"date-time":"2017-08-17T15:26:15Z","timestamp":1502983575000},"page":"A1435-A1465","source":"Crossref","is-referenced-by-count":17,"title":["ArbiLoMod, a Simulation Technique Designed for Arbitrary Local Modifications"],"prefix":"10.1137","volume":"39","author":[{"given":"Andreas","family":"Buhr","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christian","family":"Engwer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mario","family":"Ohlberger","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stephan","family":"Rave","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,8,17]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2012.02.019"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2013.01.002"},{"key":"atypb3","first-page":"406","volume":"7","author":"Albrecht F.","year":"2013","journal-title":"Oberwolfach Rep."},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2015045"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2013117"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/100795772"},{"key":"atypb7","volume-title":"Master's thesis","author":"Buhr A.","year":"2009"},{"key":"atypb8","first-page":"4094","volume-title":"Proceedings of the 11th World Congress on Computational Mechanics, X. 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Pacciarini,\n                      Discontinuous Galerkin Reduced Basis Element Methods for Parametrized Partial Differential Equations in Partitioned Domains\n                      , Ph.D. thesis, Politecnico Di Milano, Milan, Italy, 2016.","DOI":"10.1016\/j.camwa.2016.01.030"},{"key":"atypb41","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2012022"},{"key":"atypb42","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-15431-2"},{"key":"atypb43","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2014.09.020"},{"key":"atypb44","doi-asserted-by":"publisher","DOI":"10.1137\/15M1009603"},{"key":"atypb45","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-013-0576-y"},{"key":"atypb46","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(99)00072-9"},{"key":"atypb47","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(01)00188-8"},{"key":"atypb48","doi-asserted-by":"publisher","DOI":"10.1007\/b137868"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/15M1054213","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:58:07Z","timestamp":1787335087000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/15M1054213"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1]]},"references-count":48,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["10.1137\/15M1054213"],"URL":"https:\/\/doi.org\/10.1137\/15m1054213","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1]]}}}