{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,21]],"date-time":"2026-10-21T18:56:49Z","timestamp":1792609009209,"version":"4.5.0"},"reference-count":26,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"DOI":"10.13039\/100011102","name":"Seventh Framework Programme","doi-asserted-by":"publisher","award":["n600411"],"award-info":[{"award-number":["n600411"]}],"id":[{"id":"10.13039\/100011102","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>Scattering problems for periodic structures have been studied a lot in the past few years. A main idea for numerical solution methods is to reduce such problems to one periodicity cell. In contrast to periodic settings, scattering from locally perturbed periodic surfaces is way more challenging. In this paper, we introduce and analyze a new numerical method to simulate scattering from locally perturbed periodic structures based on the Bloch transform. As this transform is applied only in periodic domains, we first rewrite the scattering problem artificially in a periodic domain. With the help of the Bloch transform, we next transform this problem into a coupled family of quasi-periodic problems posed in the periodicity cell. A numerical scheme then approximates the family of quasi-periodic solutions (we rely on the finite element method) and backtransformation provides the solution to the original scattering problem. In this paper, we give convergence analysis and error bounds for a Galerkin discretization in the spatial and the quasi periodicity's unit cells. We also provide a simple and efficient way of implementation that does not require numerical integration in the quasi periodicity, together with numerical examples for scattering from locally perturbed periodic surfaces computed by this scheme.<\/jats:p>","DOI":"10.1137\/16m1104111","type":"journal-article","created":{"date-parts":[[2017,9,21]],"date-time":"2017-09-21T11:42:52Z","timestamp":1505994172000},"page":"B819-B839","source":"Crossref","is-referenced-by-count":19,"title":["A Floquet--Bloch Transform Based Numerical Method for Scattering from Locally Perturbed Periodic Surfaces"],"prefix":"10.1137","volume":"39","author":[{"given":"Armin","family":"Lechleiter","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruming","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,9,21]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-247X(02)00159-2"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1002\/mma.1670170502"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500021132"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.10.001168"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.21.000606"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/090776111"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1137\/040615523"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2011.10.022"},{"key":"atypb9","doi-asserted-by":"crossref","first-page":"849","DOI":"10.4208\/cicp.2009.v5.p849","volume":"5","author":"Ehrhardt M.","year":"2009","journal-title":"Commun. 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Analysis of Operators","author":"Reed M.","year":"1978"},{"key":"atypb26","volume-title":"Boundary Element Methods","author":"Sauter S.","year":"2007"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/16M1104111","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:07:42Z","timestamp":1787328462000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/16M1104111"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1]]},"references-count":26,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["10.1137\/16M1104111"],"URL":"https:\/\/doi.org\/10.1137\/16m1104111","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1]]}}}