Discretized Tikhonov regularization for Robin boundaries localization
We deal with a boundary detection problem arising in nondestructive testing of materials. The problem consists in recovering an unknown portion of the boundary, where a Robin condition is satisfied, with the use of a Cauchy data pair collected on the accessible part of the boundary. We combine a lin...
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| Veröffentlicht in: | Applied mathematics and computation 2014-01, Vol.226, p.374-385 |
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| container_title | Applied mathematics and computation |
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| creator | Cao, Hui Pereverzev, Sergei V. Sincich, Eva |
| description | We deal with a boundary detection problem arising in nondestructive testing of materials. The problem consists in recovering an unknown portion of the boundary, where a Robin condition is satisfied, with the use of a Cauchy data pair collected on the accessible part of the boundary. We combine a linearization argument with a Tikhonov regularization approach for the local reconstruction of the unknown defect. Moreover, we discuss the regularization parameter choice by means of the so called balancing principle and we present some numerical tests that show the efficiency of our method. |
| doi_str_mv | 10.1016/j.amc.2013.10.036 |
| format | Article |
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Moreover, we discuss the regularization parameter choice by means of the so called balancing principle and we present some numerical tests that show the efficiency of our method.</description><subject>Accessibility</subject><subject>Balancing principle</subject><subject>Boundaries</subject><subject>Free boundary problem</subject><subject>Local identification</subject><subject>Localization</subject><subject>Mathematical models</subject><subject>Nondestructive testing</subject><subject>Reconstruction</subject><subject>Recovering</subject><subject>Regularization</subject><subject>Robin boundary condition</subject><subject>Tikhonov regularization</subject><issn>0096-3003</issn><issn>1873-5649</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNp9kEFPwzAMhSMEEmPwA7j1yKUlqZO0FSc0NkCahITGOUpTFzK6ZiTtJPbrybSdOVm237OeP0JuGc0YZfJ-nemNyXLKIPYZBXlGJqwsIBWSV-dkQmklU6AULslVCGtKaSEZn5D5kw3G42D32CQr-_3lerdLPH6OnfZ2rwfr-qR1Pnl3te2T2o19ExcYks4Z3Z0U1-Si1V3Am1Odko_FfDV7SZdvz6-zx2VqoIAhFcgqjgXPOeStKGvT8EZzbHRRay3LSsqqBoMlUKhlmdNSFCY3KFAyprESMCV3x7tb735GDIPaxPjYdbpHNwbFBAMuAEQRpewoNd6F4LFVW2832v8qRtUBmVqriEwdkB1GEVn0PBw9GH_YWfQqGIu9wcZ6NINqnP3H_QfkgXSl</recordid><startdate>20140101</startdate><enddate>20140101</enddate><creator>Cao, Hui</creator><creator>Pereverzev, Sergei V.</creator><creator>Sincich, Eva</creator><general>Elsevier Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20140101</creationdate><title>Discretized Tikhonov regularization for Robin boundaries localization</title><author>Cao, Hui ; Pereverzev, Sergei V. ; Sincich, Eva</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c373t-5e194e742432f58bcd4da4eda7baa689669b3ce8303b6820857c2ce5e611ae953</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Accessibility</topic><topic>Balancing principle</topic><topic>Boundaries</topic><topic>Free boundary problem</topic><topic>Local identification</topic><topic>Localization</topic><topic>Mathematical models</topic><topic>Nondestructive testing</topic><topic>Reconstruction</topic><topic>Recovering</topic><topic>Regularization</topic><topic>Robin boundary condition</topic><topic>Tikhonov regularization</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cao, Hui</creatorcontrib><creatorcontrib>Pereverzev, Sergei V.</creatorcontrib><creatorcontrib>Sincich, Eva</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Applied mathematics and computation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Cao, Hui</au><au>Pereverzev, Sergei V.</au><au>Sincich, Eva</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Discretized Tikhonov regularization for Robin boundaries localization</atitle><jtitle>Applied mathematics and computation</jtitle><date>2014-01-01</date><risdate>2014</risdate><volume>226</volume><spage>374</spage><epage>385</epage><pages>374-385</pages><issn>0096-3003</issn><eissn>1873-5649</eissn><abstract>We deal with a boundary detection problem arising in nondestructive testing of materials. 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| ispartof | Applied mathematics and computation, 2014-01, Vol.226, p.374-385 |
| issn | 0096-3003 1873-5649 |
| language | eng |
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| source | ScienceDirect Journals (5 years ago - present) |
| subjects | Accessibility Balancing principle Boundaries Free boundary problem Local identification Localization Mathematical models Nondestructive testing Reconstruction Recovering Regularization Robin boundary condition Tikhonov regularization |
| title | Discretized Tikhonov regularization for Robin boundaries localization |
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