{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T11:51:13Z","timestamp":1773402673583,"version":"3.50.1"},"reference-count":48,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/501100005151","name":"Chinese Academy of Sciences Key Project","doi-asserted-by":"publisher","award":["2018YFB0704304"],"award-info":[{"award-number":["2018YFB0704304"]}],"id":[{"id":"10.13039\/501100005151","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013143","name":"National Natural Science Foundation of China-Shandong Joint Fund for Marine Science Research Centers","doi-asserted-by":"publisher","award":["12071468"],"award-info":[{"award-number":["12071468"]}],"id":[{"id":"10.13039\/501100013143","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013143","name":"National Natural Science Foundation of China-Shandong Joint Fund for Marine Science Research Centers","doi-asserted-by":"publisher","award":["11671391"],"award-info":[{"award-number":["11671391"]}],"id":[{"id":"10.13039\/501100013143","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013143","name":"National Natural Science Foundation of China-Shandong Joint Fund for Marine Science Research Centers","doi-asserted-by":"publisher","award":["12071149"],"award-info":[{"award-number":["12071149"]}],"id":[{"id":"10.13039\/501100013143","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003399","name":"Science and Technology Commission of Shanghai Municipality","doi-asserted-by":"publisher","award":["18dz2271000"],"award-info":[{"award-number":["18dz2271000"]}],"id":[{"id":"10.13039\/501100003399","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003399","name":"Science and Technology Commission of Shanghai Municipality","doi-asserted-by":"publisher","award":["21JC1402500"],"award-info":[{"award-number":["21JC1402500"]}],"id":[{"id":"10.13039\/501100003399","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003399","name":"Science and Technology Commission of Shanghai Municipality","doi-asserted-by":"publisher","award":["19ZR1414100"],"award-info":[{"award-number":["19ZR1414100"]}],"id":[{"id":"10.13039\/501100003399","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2022,8]]},"DOI":"10.1137\/21m1457400","type":"journal-article","created":{"date-parts":[[2022,8,15]],"date-time":"2022-08-15T16:29:53Z","timestamp":1660580993000},"page":"A2464-A2505","source":"Crossref","is-referenced-by-count":13,"title":["Improved Discrete Boundary Type Shape Gradients for PDE-constrained Shape Optimization"],"prefix":"10.1137","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3251-8771","authenticated-orcid":true,"given":"Wei","family":"Gong","sequence":"first","affiliation":[]},{"given":"Jiajie","family":"Li","sequence":"additional","affiliation":[]},{"given":"Shengfeng","family":"Zhu","sequence":"additional","affiliation":[]}],"member":"351","published-online":{"date-parts":[[2022,8,15]]},"reference":[{"key":"atypb1","first-page":"383","volume":"329","author":"Allaire G.","year":"2001","journal-title":"C. R. Acad. Sci. Paris Ser. II"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/bs.hna.2020.10.004"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/130948860"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-011-9983-3"},{"key":"atypb5","volume-title":"Topology Optimization. Theory, Methods and Applications","author":"Bends\u00f8e M. P.","year":"2003"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/978-90-481-3239-3_4"},{"key":"atypb7","unstructured":"B. Bogosel,Shape Optimization and Spectral Problems, Ph.D. thesis, Universit\u00e9 Grenoble Alpes, 2015."},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7643-8923-9_2"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-75934-0"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1137\/19M1268628"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.4171\/IFB\/81"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1002\/nme.824"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1986200303711"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/j.anihpc.2014.09.007"},{"key":"atypb15","volume-title":"Analysis, Differential Calculus, and Optimization","author":"Delfour M. C.","year":"2011","edition":"2"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-020-02742-w"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1137\/20M1323898"},{"key":"atypb18","volume-title":"M\u00e9moires pr\u00e9sent\u00e9s par divers savants \u00e0 l'Acad\u00e9mie des Sciences 33","author":"Hadamard J.","year":"1908"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1137\/110855703"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718690"},{"key":"atypb21","volume-title":"Finite Element Approximation for Optimal Shape, Material and Topology Design","author":"Haslinger J.","year":"1996","edition":"2"},{"key":"atypb22","volume-title":"Design Sensitivity Analysis of Structural Systems","author":"Haug E. J.","year":"1986"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1007\/3-7643-7706-2"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-014-0515-z"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1515\/jnum-2012-0013"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1137\/17M1152711"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.2010.244.99"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2015075"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2019.04.002"},{"key":"atypb30","volume-title":"Applied Shape Optimization for Fluids","author":"Mohammadi B.","year":"2010","edition":"2"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(88)90002-2"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1051\/cocv:2004011"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2010.07.040"},{"key":"atypb34","doi-asserted-by":"crossref","first-page":"987","DOI":"10.57262\/ade\/1357140555","volume":"6","author":"Ortega J. H.","year":"2001","journal-title":"Adv. Differential Equations"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-17563-8_9"},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-020-02813-y"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-87722-3"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1515\/cmam-2016-0009"},{"key":"atypb39","doi-asserted-by":"publisher","DOI":"10.1137\/140985883"},{"key":"atypb40","doi-asserted-by":"publisher","DOI":"10.1137\/15M1029369"},{"key":"atypb41","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-58106-9"},{"key":"atypb42","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(02)00559-5"},{"key":"atypb43","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2007.06.006"},{"key":"atypb44","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-017-0451-6"},{"key":"atypb45","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-017-1198-9"},{"key":"atypb46","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2018.08.024"},{"key":"atypb47","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-019-00782-3"},{"key":"atypb48","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620330702"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","deposited":{"date-parts":[[2023,2,14]],"date-time":"2023-02-14T22:53:14Z","timestamp":1676415194000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/21M1457400"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8]]},"references-count":48,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,8]]}},"alternative-id":["10.1137\/21M1457400"],"URL":"https:\/\/doi.org\/10.1137\/21m1457400","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8]]}}}