{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,29]],"date-time":"2026-08-29T00:22:30Z","timestamp":1787962950573,"version":"build-2784847793"},"reference-count":40,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Math."],"published-print":{"date-parts":[[2013,1]]},"abstract":"<jats:p>This paper is concerned with the direct and inverse acoustic or electromagnetic scattering problems by a locally perturbed, perfectly reflecting, infinite plane (which is called a locally rough surface in this paper). We propose a novel integral equation formulation for the direct scattering problem which is defined on a bounded curve (consisting of a bounded part of the infinite plane containing the local perturbation and the lower part of a circle) with two corners. This novel integral equation can be solved efficiently by using the Nystr\u00f6m method with a graded mesh introduced previously by Kress and is capable of dealing with large wave number cases. For the inverse problem, we propose a Newton iteration method to reconstruct the local perturbation of the plane from multiple-frequency far-field data, based on the novel integral equation formulation. Numerical examples are carried out to demonstrate that our reconstruction method is stable and accurate even for the case of multiple-scale profiles.<\/jats:p>","DOI":"10.1137\/130908324","type":"journal-article","created":{"date-parts":[[2013,9,11]],"date-time":"2013-09-11T03:42:40Z","timestamp":1378870960000},"page":"1811-1829","source":"Crossref","is-referenced-by-count":45,"title":["A Novel Integral Equation for Scattering by Locally Rough Surfaces and Application to the Inverse Problem"],"prefix":"10.1137","volume":"73","author":[{"given":"Haiwen","family":"Zhang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bo","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2013,9,10]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1080\/00036819008839905"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1002\/1099-1476(200008)23:12<1057::AID-MMA151>3.0.CO;2-6"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/4.1.19"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.4208\/nmtma.2011.m1021"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.3934\/ipi.2013.7.377"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/110824644"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1364\/OL.37.005027"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827503428539"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1002\/num.20643"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2001.0882"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/26\/4\/045007"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139996309722"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1999.0476"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/040615523"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2006.1752"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1137\/050635262"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1137\/090776111"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1007\/s00607-004-0109-8"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1216\/JIE-2009-21-2-229"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1088\/0959-7174\/9\/3\/311"},{"key":"atypb21","unstructured":"D. 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