{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T11:33:19Z","timestamp":1770723199201,"version":"3.49.0"},"reference-count":37,"publisher":"Walter de Gruyter GmbH","issue":"4","funder":[{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-20-1-0024"],"award-info":[{"award-number":["FA9550-20-1-0024"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The time domain linear sampling method (TD-LSM) solves inverse scattering problems using time domain data by creating an indicator function for the support of the unknown scatterer. It involves only solving a\nlinear integral equation called the near-field equation using different data from sampling points that probe the domain where the scatterer is located. To date,\nthe method has been used for the acoustic wave equation and has been tested for several different types of scatterers, i.e. sound hard, impedance, and\npenetrable, and for waveguides. In this paper, we extend the TD-LSM to the time dependent Maxwell\u2019s system with impedance boundary conditions \u2013 a\nsimilar analysis handles the case of a perfect electric conductor (PEC). We provide an analysis that supports the use of the TD-LSM for this problem, and preliminary numerical tests of the algorithm. Our analysis\nrelies on the Laplace transform approach previously used for the acoustic wave equation. This is the first application of the TD-LSM in electromagnetism.<\/jats:p>","DOI":"10.1515\/cmam-2021-0190","type":"journal-article","created":{"date-parts":[[2022,7,13]],"date-time":"2022-07-13T08:52:27Z","timestamp":1657702347000},"page":"889-913","source":"Crossref","is-referenced-by-count":5,"title":["The Time Domain Linear Sampling Method for Determining the Shape of Multiple Scatterers Using Electromagnetic Waves"],"prefix":"10.1515","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0719-1973","authenticated-orcid":false,"given":"Timo","family":"L\u00e4hivaara","sequence":"first","affiliation":[{"name":"Department of Applied Physics , University of Eastern Finland , 70211 Kuopio , Finland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6539-5897","authenticated-orcid":false,"given":"Peter","family":"Monk","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences , University of Delaware , Newark , DE 19716 , USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0567-5766","authenticated-orcid":false,"given":"Virginia","family":"Selgas","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas , Universidad de Oviedo , EPIG, C\/ Luis Ortiz Berrocal s\/n, 33203 Gij\u00f3n , Spain"}]}],"member":"374","published-online":{"date-parts":[[2022,5,31]]},"reference":[{"key":"2023033113381577220_j_cmam-2021-0190_ref_001","doi-asserted-by":"crossref","unstructured":"A.  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