{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:34:33Z","timestamp":1787337273473,"version":"build-2736575974"},"reference-count":11,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>We analyze an optimal design problem in three-dimensional (3D) heat conduction: Given fixed amounts of two isotropic conducting materials, decide how we are to mix them in a 3D domain to minimize the quadratic mean temperature gradient. By using an optimality criteria method, we provide some numerical evidence that Tartar's result (see [in Calculus of Variations, Homogenization and Continuum Mechanics, G. Buttazzo, G. Bouchitte, and P. Suquet, eds., World Scientific, River Edge, NJ, 1994, pp. 279-296]) is verified in three dimensions when the target vector field is zero.<\/jats:p>","DOI":"10.1137\/060650453","type":"journal-article","created":{"date-parts":[[2006,8,24]],"date-time":"2006-08-24T15:29:50Z","timestamp":1156433390000},"page":"929-941","source":"Crossref","is-referenced-by-count":10,"title":["Numerical Simulations in 3D Heat Conduction: Minimizing the Quadratic Mean Temperature Gradient by an Optimality Criteria Method"],"prefix":"10.1137","volume":"28","author":[{"given":"Alberto","family":"Donoso","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,8,4]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9286-6"},{"key":"R2","unstructured":"S. Aubry,\n                      Etude th\u00e9roique et num\u00e9rique de quelques probl\u00e8mes d\u2019optimisation de forme \u00e0 l\u2019aide de m\u00e9thodes d\u2019homog\u00e9n\u00e9isation\n                      , Ph.D thesis, Paris 6 University, Paris, 1999."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-3376-3"},{"key":"R4","volume-title":"Topology optimization","author":"Bends\u00f8e M.","year":"2003"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(02)00284-5"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-005-0521-5"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1006\/aama.2001.0757"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"Robert Lipton, Ani Velo, Optimal design of gradient fields with applications to electrostatics, Stud. Math. Appl., Vol. 31, North\u2010Holland, Amsterdam, 2002, 509\u20135322003j:78018","DOI":"10.1016\/S0168-2024(02)80024-8"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/BF02413475"},{"key":"R10","unstructured":"P. Pedregal,\n                      Optimal design in 2\u2010d conductivity for quadratic functionals in the field\n                      , in Proceedings of the NATO Advanced Workshop in Nonlinear Homogenization, Warsaw, 2003."},{"key":"R11","unstructured":"Luc Tartar, Remarks on optimal design problems, Ser. Adv. Math. Appl. Sci., Vol. 18, World Sci. Publishing, River Edge, NJ, 1994, 279\u20132961428706"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/060650453","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:53:48Z","timestamp":1787334828000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/060650453"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":11,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1137\/060650453"],"URL":"https:\/\/doi.org\/10.1137\/060650453","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}