{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:29:41Z","timestamp":1787333381371,"version":"build-2736575974"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[1998,11]]},"abstract":"<jats:p>The purpose of this paper is to study the optimal design problem of a nonsmooth shape, applied to linear acoustics in a bounded domain. Within the classical Helmholtz model, we consider the maximum of the acoustical pressure in a prescribed sensitive area as cost function to be minimized. A given part of the boundary of the domain is considered as the design variable. The existence of subgradients is demonstrated, and a technique for computing them is described. It turns out that the classical (differentiable) sensitivity subroutines could be used in order to compute subgradients.<\/jats:p>\n                  <jats:p>\n                    The numerical results presented tend to show that the acoustical pressure is not very sensitive to small changes of the shape for low frequencies, but it is sensitive for medium frequencies, and one obtains an optimal shape for the L\n                    <jats:sup>2<\/jats:sup>\n                    cost that is slightly different from the one obtained for the L{\\infty}$ cost.\n                  <\/jats:p>","DOI":"10.1137\/s105262349529581x","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"989-1006","source":"Crossref","is-referenced-by-count":13,"title":["Nonsmooth Shape Optimization Applied to Linear Acoustics"],"prefix":"10.1137","volume":"8","author":[{"given":"Abderrahmane","family":"Habbal","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"N.Peake, D.Crighton, Active control of sound, Annu. Rev. Fluid Mech., Vol. 32, Annual Reviews, Palo Alto, CA, 2000, 137\u20131641744306","DOI":"10.1146\/annurev.fluid.32.1.137"},{"key":"R2","unstructured":"D. Duhamel,\n                      L\u2019acoustique des probl\u00e8mes coupl\u00e9s fluide\u2010structure. application au controle actif du son\n                      , Th\u00e8se de Doctorat, Ecole Nationale des Ponts et Chaussees, Paris, France, 1994."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/0323040"},{"key":"R4","volume-title":"Interactions fluides\u2010structures","author":"Morand Henri","year":"1992"},{"key":"R5","unstructured":"N. S. Trudinger and D. Gilbarg,\n                      Elliptic Partial Differential Equations of Second Order\n                      , Springer\u2010Verlag, Berlin, Heidelberg, New York, 1977."},{"key":"R6","unstructured":"B. Rousselet,\n                      Quelques r\u00e9sultats en optimisation de domaines\n                      , Th\u00e8se de Doctorat d\u2019Etat, Universit\u00e9 de Nice\u2013Sophia Antipolis, Nice, France, 1982."},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6377(99)00063-2"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"J. B. Hiriart\u2010Urruty and C. Lemar\u00e9chal,\n                      Convex Analysis and Minimization Algorithms I and II\n                      , Springer\u2010Verlag, Berlin, Heidelberg, 1993.","DOI":"10.1007\/978-3-662-02796-7"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"C.Lemarechal, J.\u2010J.Strodiot, A.Bihain, On a bundle algorithm for nonsmooth optimization, Academic Press, New York, 1981, 245\u201328283k:90102","DOI":"10.1016\/B978-0-12-468662-5.50015-X"},{"key":"R10","unstructured":"F. H. Clarke,\n                      Optimization and Nonsmooth Analysis\n                      , Wiley, New York, 1983."},{"key":"R11","unstructured":"M. M. Makela and P. Neittaanmaki,\n                      Nonsmooth Optimization: Analysis and Algorithms with Applications to Optimal Control\n                      , World Scientific, Singapore, 1992."},{"key":"R12","unstructured":"ClaudeLemarechal, Nondifferentiable optimization, Birkh\u00e4user Boston, Mass., 1980, 149\u201319983c:90152"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1986200303711"},{"key":"R14","unstructured":"M. Masmoudi,\n                      Outils pour la Conception Optimale de Forme\n                      , Th\u00e8se d\u2019Etat, University of Nice, Nice, France, 1987."},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1080\/08905459208905162"},{"key":"R16","unstructured":"J. Necas,\n                      Les M\u00e9thodes Directes en Th\u00e9orie des Equations Elliptiques\n                      , Masson, Paris, France, 1967."},{"key":"R17","unstructured":"J. Simon and F. Murat,\n                      Sur le Contr\u00f4le par un Domaine G\u00e9ometrique\n                      , Th\u00e8se d\u2019Etat, Universit\u00e9 Paris 6, Paris, France, 1976."},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-87722-3"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1137\/0802008"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1007\/BF01585731"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S105262349529581X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:55:05Z","timestamp":1787331305000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S105262349529581X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,11]]},"references-count":20,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1998,11]]}},"alternative-id":["10.1137\/S105262349529581X"],"URL":"https:\/\/doi.org\/10.1137\/s105262349529581x","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,11]]}}}