{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:34:49Z","timestamp":1787337289224,"version":"build-2736575974"},"reference-count":10,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>The goal of this work is the numerical realization of the probe method suggested by Ikehata for the detection of an obstacle D in inverse scattering. The main idea of the method is to use probes in the form of point source $\\Phi(\\cdot,z)$ with source point z to define an indicator function $\\hat{I}(z)$ which can be reconstructed from Cauchy data or far field data. The indicator function $\\hat{I}(z)$ can be shown to blow off when the source point z tends to the boundary $\\partial D$, and this behavior can be used to find D. To study the feasibility of the probe method we will use two equivalent formulations of the indicator function. We will carry out the numerical realization of the functional and show reconstructions of a sound\u2010soft obstacle.<\/jats:p>","DOI":"10.1137\/040607149","type":"journal-article","created":{"date-parts":[[2006,11,28]],"date-time":"2006-11-28T18:05:07Z","timestamp":1164737107000},"page":"1597-1612","source":"Crossref","is-referenced-by-count":16,"title":["A Numerical Study of the Probe Method"],"prefix":"10.1137","volume":"28","author":[{"given":"Klaus","family":"Erhard","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Roland","family":"Potthast","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,9,29]]},"reference":[{"key":"R1","unstructured":"J. Cheng, J. Liu, and G. Nakamura,\n                      Recovery of Boundaries and Types for Multiple Obstacles from the Far\u2010Field Pattern\n                      , EPrint Series, Department of Mathematics, Hokkaido University, Sapporo, Japan, 2005. Available online at http:\/\/eprints.math.sci. hokudai.ac.jp\/archive\/00000982\/."},{"key":"R2","doi-asserted-by":"crossref","unstructured":"D. Colton and R. Kress,\n                      Inverse Acoustic and Electromagnetic Scattering Theory\n                      , 2nd ed., Appl. Math. Sci. 93, Springer\u2010Verlag, Berlin, 1998.","DOI":"10.1007\/978-3-662-03537-5"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/19\/5\/308"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/14\/4\/012"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1080\/03605309808821390"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-2125(99)00006-2"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(94)00073-7"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01328780"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"R. Potthast,\n                      Point Sources and Multipoles in Inverse Scattering Theory\n                      , Chapman & Hall\/CRC Research Notes in Mathematics 427, Chapman & Hall\/CRC, Boca Raton, FL, 2001.","DOI":"10.1201\/9781420035483"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/s00607-004-0084-0"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/040607149","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:54:56Z","timestamp":1787334896000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/040607149"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":10,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1137\/040607149"],"URL":"https:\/\/doi.org\/10.1137\/040607149","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}