{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T08:42:33Z","timestamp":1781167353429,"version":"3.54.1"},"reference-count":59,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2025,8,7]],"date-time":"2025-08-07T00:00:00Z","timestamp":1754524800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"National Science Foundation","award":["DMS-2111474"],"award-info":[{"award-number":["DMS-2111474"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,3,26]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We present an approach to shape optimization problems that uses an unfitted finite element method (FEM). The domain geometry is represented, and optimized, using a (discrete) level set function and we consider objective functionals that are defined over bulk domains. For a discrete objective functional, defined in the unfitted FEM framework, we show that the\n                    <jats:italic>exact<\/jats:italic>\n                    discrete shape derivative essentially matches the shape derivative at the continuous level. In other words, our approach has the benefits of both optimize-then-discretize and discretize-then-optimize approaches. Specifically, we establish the shape Fr\u00e9chet differentiability of discrete (unfitted) bulk shape functionals using both the perturbation of the identity approach and direct perturbation of the level set representation. The latter approach is especially convenient for optimizing with respect to level set functions. Moreover, our Fr\u00e9chet differentiability results hold for\n                    <jats:italic>any<\/jats:italic>\n                    polynomial degree used for the discrete level set representation of the domain. We illustrate our results with some numerical accuracy tests, a simple model (geometric) problem with known exact solution, as well as shape optimization of structural designs.\n                  <\/jats:p>","DOI":"10.1515\/jnma-2024-0113","type":"journal-article","created":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T11:03:33Z","timestamp":1754478213000},"page":"91-124","source":"Crossref","is-referenced-by-count":2,"title":["Exact shape derivatives with unfitted finite element methods"],"prefix":"10.1515","volume":"34","author":[{"given":"Jeremy T.","family":"Shahan","sequence":"first","affiliation":[{"name":"Department of Mathematics , 5779 Louisiana State University , Baton Rouge , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shawn W.","family":"Walker","sequence":"additional","affiliation":[{"name":"Department of Mathematics , 5779 Louisiana State University , Baton Rouge , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","published-online":{"date-parts":[[2025,8,7]]},"reference":[{"key":"2026030615521516017_j_jnma-2024-0113_ref_001","doi-asserted-by":"crossref","unstructured":"J. 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