{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:31:27Z","timestamp":1777447887549,"version":"3.51.4"},"reference-count":20,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2018,1,22]],"date-time":"2018-01-22T00:00:00Z","timestamp":1516579200000},"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":["Asymptotic Analysis"],"published-print":{"date-parts":[[2018,1,22]]},"abstract":"<jats:p>We consider the two-dimensional steady-state heat conduction on a bounded domain \u03a9 containing a heat source at an unknown location [Formula: see text]. We are interested in determining the locations \u03c9 allowing a suitable thermal environment. The resulting shape optimization problem consists of a geometric control of either the maximum of the temperature or its [Formula: see text] mean oscillations in \u03a9. We derive the topological asymptotic expansion of the considered shape functionals with respect to the insertion of small circular coated inclusion characterized by a discontinuous thermal conductivity and their radius. We propose a reconstruction algorithm based on this topological gradient to identify the locations. Some numerical simulations are presented to show the efficiency of the algorithm.<\/jats:p>","DOI":"10.3233\/asy-171441","type":"journal-article","created":{"date-parts":[[2018,1,23]],"date-time":"2018-01-23T11:28:46Z","timestamp":1516706926000},"page":"99-119","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":4,"title":["Topology optimization method with respect to the insertion of small coated inclusion"],"prefix":"10.1177","volume":"106","author":[{"given":"Z.","family":"Belhachmi","sequence":"first","affiliation":[{"name":"Mathematics, Information Technology and Applications Laboratory (LMIA, EA 3993), 4 rue des Fr\u00e8res Lumi\u00e8re, 68093 Mulhouse, Cedex, France. E-mail:\u00a0"}]},{"given":"A.","family":"Ben Abda","sequence":"additional","affiliation":[{"name":"Laboratoire de Mod\u00e9lisation Math\u00e9matiques et Num\u00e9riques dans les Sciences de L\u2019ing\u00e9nieurs, Universit\u00e9 Tunis El-Manar, Tunis. E-mails:\u00a0,\u00a0"}]},{"given":"B.","family":"Meftahi","sequence":"additional","affiliation":[{"name":"Laboratoire de Mod\u00e9lisation Math\u00e9matiques et Num\u00e9riques dans les Sciences de L\u2019ing\u00e9nieurs, Universit\u00e9 Tunis El-Manar, Tunis. E-mails:\u00a0,\u00a0"}]},{"given":"H.","family":"Meftahi","sequence":"additional","affiliation":[{"name":"Technical University of Berlin, Str. des 17. Juni 136, 10623 Berlin, Germany. E-mail:\u00a0"}]}],"member":"179","published-online":{"date-parts":[[2018,1,22]]},"reference":[{"key":"ref001","unstructured":"G.\u00a0Allaire, Shape Optimization by the Homogenization Method, Vol.\u00a0146, Springer Science & Business Media, 2012."},{"key":"ref002","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139900369266"},{"key":"ref003","doi-asserted-by":"crossref","unstructured":"H.\u00a0Ammari, E.\u00a0Bretin, J.\u00a0Garnier, H.\u00a0Kang, H.\u00a0Lee and A.\u00a0Wahab, Mathematical Methods in Elasticity Imaging, Princeton University Press, 2015.","DOI":"10.23943\/princeton\/9780691165318.001.0001"},{"key":"ref004","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-09-04842-9"},{"key":"ref005","doi-asserted-by":"publisher","DOI":"10.3233\/ASY-2006-778"},{"key":"ref006","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2009013"},{"key":"ref007","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2008.07.002"},{"key":"ref008","doi-asserted-by":"publisher","DOI":"10.1007\/b137163"},{"key":"ref009","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/14\/3\/011"},{"key":"ref010","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2012.11.044"},{"key":"ref011","doi-asserted-by":"publisher","DOI":"10.1007\/s00791-014-0219-6"},{"key":"ref012","doi-asserted-by":"publisher","DOI":"10.1137\/15100477X"},{"key":"ref013","doi-asserted-by":"publisher","DOI":"10.1137\/100812501"},{"key":"ref014","unstructured":"S.\u00a0Garreau, P.\u00a0Guillaume and M.\u00a0Masmoudi, The topological sensitivity for linear isotropic elasticity,\n                      ECCMa\n                      99\n                      (1999)."},{"key":"ref015","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-37689-5"},{"key":"ref016","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-2032-9_6"},{"key":"ref017","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(02)00599-6"},{"key":"ref018","unstructured":"O.\u00a0Pironneau, Optimal Shape Design for Elliptic Systems, Springer Science & Business Media, 2012."},{"key":"ref019","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-58106-9_1"},{"key":"ref020","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2000101"}],"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-171441","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/ASY-171441","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-171441","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:36:08Z","timestamp":1777379768000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-171441"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,22]]},"references-count":20,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,1,22]]}},"alternative-id":["10.3233\/ASY-171441"],"URL":"https:\/\/doi.org\/10.3233\/asy-171441","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1,22]]}}}