{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T03:13:57Z","timestamp":1777000437739,"version":"3.51.4"},"reference-count":15,"publisher":"Walter de Gruyter GmbH","issue":"4","funder":[{"name":"Endress+Hauser Flowtec AG Reinach"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Two optimal control problems for instationary magnetization\nprocesses are considered in 3D spatial domains that\ninclude electrically conducting and nonconducting regions. The magnetic\nfields are generated by induction coils. In the first model, the induction coil\nis considered as part of the conducting region and the electrical current is taken\nas control. In the second, the coil is viewed as part of the nonconducting region and the\nelectrical voltage is the control.\nHere, an integro-differential equation accounts for the magnetic induction law that couples the given\nelectrical voltage with the induced electrical current in the induction coil.\nWe derive first-order necessary optimality conditions for the optimal controls of both problems. Based on them,\nnumerical methods of gradient type are applied. Moreover, we report on the application\nof model reduction by POD that lead to tremendous savings. Numerical tests are\npresented for academic 3D geometries but also for a real-world application.<\/jats:p>","DOI":"10.1515\/cmam-2014-0022","type":"journal-article","created":{"date-parts":[[2014,8,19]],"date-time":"2014-08-19T17:01:00Z","timestamp":1408467660000},"page":"555-573","source":"Crossref","is-referenced-by-count":19,"title":["On Two Optimal Control Problems for Magnetic Fields"],"prefix":"10.1515","volume":"14","author":[{"given":"Serge","family":"Nicaise","sequence":"first","affiliation":[{"name":"LAMAV and FR CNRS 2956, Universit\u00e9 de Valenciennes et du Hainaut Cambr\u00e9sis, Institut des Sciences et Techniques of Valenciennes, 59313 Valenciennes Cedex 9, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Simon","family":"Stingelin","sequence":"additional","affiliation":[{"name":"ZHAW School of Engineering, Institut f\u00fcr Angewandte Mathematik und Physik (IAMP), Technikumstrasse 9, Postfach, 8401 Winterthur, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fredi","family":"Tr\u00f6ltzsch","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, 10623 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2014,8,20]]},"reference":[{"key":"ref41","doi-asserted-by":"crossref","first-page":"1707","DOI":"10.1137\/090760544","article-title":"Optimal control of three - 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