{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T16:03:37Z","timestamp":1791302617541,"version":"4.1.0"},"reference-count":28,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2003,1]]},"abstract":"<jats:p>The aim of the topological sensitivity analysis is to obtain an asymptotic expansion of a functional with respect to the creation of a small hole in the domain. In this paper such an expansion is obtained for the Helmholtz equation with a Dirichlet condition on the boundary of a circular hole. Some applications of this work to waveguide optimization are presented.<\/jats:p>","DOI":"10.1137\/s0363012902406801","type":"journal-article","created":{"date-parts":[[2003,11,10]],"date-time":"2003-11-10T21:00:45Z","timestamp":1068498045000},"page":"1523-1544","source":"Crossref","is-referenced-by-count":93,"title":["The Topological Asymptotic for the Helmholtz Equation"],"prefix":"10.1137","volume":"42","author":[{"given":"Bessem","family":"Samet","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Samuel","family":"Amstutz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohamed","family":"Masmoudi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","unstructured":"M. Abramowitz and I. A. Stegun,\n                      Handbook of Mathematical Functions\n                      , Dover, New York, 1964."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1090\/qam\/1247433"},{"key":"R3","first-page":"839","volume":"12","author":"Allaire G.","year":"1993","journal-title":"European J. Mech. A Solids"},{"key":"R4","unstructured":"M. Becker,\n                      Optimisation topologique de structure en variables discr\u00e8tes\n                      , Technical report, Universit\u00e9 de Li\u00e8ges, Li\u00e8ges, Belgium, 1996."},{"key":"R5","unstructured":"M. Bendsoe,\n                      Optimal Topology Design of Continuum Structure: An Introduction\n                      , Technical report, Department of Mathematics, Technical University of Denmark, Lyngby, Denmark, 1996."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/BF01442391"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1986200303711"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1007\/BF02575843"},{"key":"R9","volume-title":"Analyse math\u00e9matique et calcul num\u00e9rique pour les sciences et les techniques. Tome 1","author":"Dautray Robert","year":"1984"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012900369538"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012901384193"},{"key":"R12","unstructured":"Ph. Guillaume and K. Sid Idris,\n                      Topological sensitivity and shape optimization for the Stokes equations\n                      , Numer. Math., submitted."},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050025"},{"key":"R14","unstructured":"P. Guillaume,\n                      D\u00e9riv\u00e9es d\u2019ordre sup\u00e9rieur en conception optimale de forme\n                      , Th\u00e8se, Universit\u00e9 Paul Sabatier, Toulouse, France, 1994."},{"key":"R15","unstructured":"J. Jacobsen, N. Olhoff, and E. Ronholt,\n                      Generalized Shape Optimization of Three\u2010Dimensional Structures Using Materials with Optimum Microstructures\n                      , Technical report, Institute of Mechanical Engineering, Aalborg University, Aalborg, Denmark, 1996."},{"key":"R16","unstructured":"M. Masmoudi,\n                      The topological asymptotic\n                      , in Computational Methods for Control Applications, R. Glowinski, H. Kawarada, and J. Periaux, eds., GAKUTO Internat. Ser. Math. Sci. Appl. 16, Tokyo, Japan, 2001, pp. 53\u201372."},{"key":"R17","unstructured":"M. Masmoudi,\n                      Outils pour la conception optimale de formes\n                      , Th\u00e8se d\u2019\u00e9tat, Universit\u00e9 de Nice, Sophia\u2010Antipolis, France, 1987."},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1007\/BF01399696"},{"key":"R19","unstructured":"M. Masmoudi,\n                      R\u00e9solution num\u00e9rique de probl\u00e8mes exterieurs\n                      , Th\u00e8se pr\u00e9sent\u00e9e \u00e0 l\u2019universit\u00e9 de Nice, Sophia\u2010Antipolis, France, 1979."},{"key":"R20","unstructured":"F. Murat and J. Simon,\n                      Sur le contr\u00f4le par un domaine g\u00e9om\u00e9trique\n                      , Th\u00e8se d\u2019\u00e9tat, Universit\u00e9 Pierre et Marie Curie, Paris, 1976."},{"key":"R21","unstructured":"F. Murat and L. Tartar,\n                      Calcul des variations et homog\u00e9n\u00e9isation\n                      , in Les m\u00e9thodes de l\u2019homog\u00e9n\u00e9isation: Th\u00e9orie et Applications en Physique, Eyrolles, Paris, 1985, pp. 319\u2013369."},{"key":"R22","unstructured":"P. Mader,\n                      Optimisation topologique pour la conception de composants guid\u00e9s\n                      , Th\u00e8se, Universit\u00e9 Paul Sabatier, Toulouse, France, 2002."},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4393-7"},{"key":"R24","unstructured":"P. A. Raviart and J. M. Thomas,\n                      Introduction \u00e0 l\u2019analyse num\u00e9rique des \u00e9quations aux d\u00e9riv\u00e9es partielles\n                      , Masson, Paris, 1988."},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012997323230"},{"key":"R26","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1080\/12506559.1996.10511240","volume":"5","author":"Schoenauer Marc","year":"1996","journal-title":"Rev. Europ\u00e9enne \u00c9l\u00e9m. Finis"},{"key":"R27","unstructured":"A. Schumacher,\n                      Topologieoptimierung von Bauteilstrukturen unter Verwendung von Lopchpositionierungkrieterien\n                      , Ph.D. thesis, Universit\u00e4t\u2010Gesamthochschule Siegen, Siegen, Germany, 1995."},{"key":"R28","unstructured":"Ch. Vassallo,\n                      Th\u00e9orie des guides d\u2019ondes \u00e9lectromagn\u00e9tiques\n                      , Collection Technique et scientifique des Tel\u00e9communications, Eyrolles, Paris, 1985."}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0363012902406801","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:24:13Z","timestamp":1787318653000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0363012902406801"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,1]]},"references-count":28,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2003,1]]}},"alternative-id":["10.1137\/S0363012902406801"],"URL":"https:\/\/doi.org\/10.1137\/s0363012902406801","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,1]]}}}