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Finally, we show how the topological derivative in conjunction with a level set method on the surface can be used to solve the topology optimization problem numerically.<\/jats:p>","DOI":"10.1137\/20m1339040","type":"journal-article","created":{"date-parts":[[2022,1,4]],"date-time":"2022-01-04T10:23:24Z","timestamp":1641291804000},"page":"81-103","source":"Crossref","is-referenced-by-count":9,"title":["Topological Derivative for PDEs on Surfaces"],"prefix":"10.1137","volume":"60","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8906-821X","authenticated-orcid":true,"given":"Peter","family":"Gangl","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9855-739X","authenticated-orcid":true,"given":"Kevin","family":"Sturm","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2022,1,4]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"P.A. Absil, R. Mahony, and R. Sepulchre,\n                      Optimization Algorithms on Matrix Manifolds\n                      , Princeton University Press, Princeton, NJ, 2008.","DOI":"10.1515\/9781400830244"},{"key":"atypb2","doi-asserted-by":"crossref","first-page":"87","DOI":"10.3233\/ASY-2006-778","volume":"49","author":"Amstutz S.","year":"2006","journal-title":"Asymptotic Anal."},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2005.12.015"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1553\/etna_vol51s169"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2010010"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/aa5c0a"},{"key":"atypb7","unstructured":"Y. Deng, W. Zhang, J. Zhu, J. Bai, Z. Liu, and J. Korvink,\n                      Topology Optimization of Surface Flows\n                      , preprint,arXiv:2002.06842, 2020."},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.5802\/aif.55"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01742933"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2020035"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012900369538"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1307\/mmj\/1029001150"},{"key":"atypb13","first-page":"913","volume":"37","author":"Hinterm\u00fcller M.","year":"2008","journal-title":"Control Cybernet."},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1007\/s10444-011-9205-4"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/j.finel.2016.06.003"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.4171\/ZAA\/1429"},{"key":"atypb17","unstructured":"T. Lewinski and J. Sokolowski,\n                      Optimal Shells Formed on a Sphere. The Topological Derivative Method\n                      , Research Report RR-3495, INRIA, 1998,https:\/\/hal.inria.fr\/inria-00073191."},{"key":"atypb18","doi-asserted-by":"crossref","unstructured":"A. A. Novotny and J. Soko\u0142owski,\n                      Topological Derivatives in Shape Optimization\n                      , Springer, Berlin, 2013,https:\/\/doi.org\/10.1007\/978-3-642-35245-4.","DOI":"10.1007\/978-3-642-35245-4"},{"key":"atypb19","unstructured":"C. Ortner and E. S\u00fcli,\n                      A Note on Linear Elliptic Systems on $\\mathbb{R}^d$\n                      , preprint,arXiv:1202.3970, 2012."},{"key":"atypb20","unstructured":"T. Patterson and N. V. Kelso,\n                      Natural Earth\n                      ,https:\/\/www.naturalearthdata.com\/downloads\/110m-physical-vectors\/110m-land\/, accessed: May 7, 2020."},{"key":"atypb21","unstructured":"J. Sch\u00f6berl,\n                      C++11 Implementation of Finite Elements in NGSolve\n                      , Tech. Report 30, Institute for Analysis and Scientific Computing, Vienna University of Technology, Vienna, Austria, 2014."},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012997323230"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6544\/ab86cb"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/20M1339040","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:41:59Z","timestamp":1787316119000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/20M1339040"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,4]]},"references-count":23,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,2]]}},"alternative-id":["10.1137\/20M1339040"],"URL":"https:\/\/doi.org\/10.1137\/20m1339040","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,4]]}}}