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Identification of discontinuous coefficients in elliptic problems using total variation regularization.

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Identification of discontinuous coefficients in elliptic problems using total variation regularization.

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dc.contributor.author Chan, Tony F.
dc.contributor.author Tai, Xue Cheng.
dc.date.accessioned 2009-05-12T08:57:35Z
dc.date.available 2009-05-12T08:57:35Z
dc.date.copyright 2003
dc.date.issued 2009-05-12T08:57:35Z
dc.identifier.citation Chan, T. F., & Tai, X. C. (2003). Identification of discontinuous coefficients in elliptic problems using total variation regularization. SIAM Journal on Scientific Computing, 25(3), 881–904.
dc.identifier.issn 1095-7197
dc.identifier.uri http://hdl.handle.net/10220/4605
dc.description.abstract We propose several formulations for recovering discontinuous coefficients in elliptic problems by using total variation (TV) regularization. The motivation for using TV is its well-established ability to recover sharp discontinuities. We employ an augmented Lagrangian variational formulation for solving the output-least-squares inverse problem. In addition to the basic output-least-squares formulation, we introduce two new techniques for handling large observation errors. First, we use a filtering step to remove as much of the observation error as possible. Second, we introduce two extensions of the output-least-squares model; one model employs observations of the gradient of the state variable while the other uses the flux. Numerical experiments indicate that the combination of these two techniques enables us to successfully recover discontinuous coefficients even under large observation errors.
dc.format.extent 24 p.
dc.language.iso en
dc.relation.ispartofseries SIAM journal on scientific computing
dc.rights SIAM Journal on Scientific Computing @ 2003 Society for Industrial and Applied Mathematics (SIAM). The journal's website is located at http://siamdl.aip.org/vsearch/servlet/VerityServlet?KEY=SIAMDL&smode=results&sort=rel&maxdisp=25&threshold=0&pjournals=SIAMDL%2CMMSUBT%2CSJADAY%2CSMJMAP%2CSMJCAT%2CSJCODC%2CSJDMEC%2CSJISBI%2CSJMAAH%2CSJMAEL%2CSJNAAM%2CSJOPE8%2CSJOCE3%2CSIREAD%2CTPRBAU&possible1=Identification+of+discontinuous&possible1zone=article&OUTLOG=NO&viewabs=SJOCE3&key=DISPLAY&docID=1&page=0&chapter=0.
dc.subject DRNTU::Science::Mathematics::Analysis.
dc.title Identification of discontinuous coefficients in elliptic problems using total variation regularization.
dc.type Journal Article
dc.contributor.school School of Physical and Mathematical Sciences
dc.identifier.openurl http://sfxna09.hosted.exlibrisgroup.com:3410/ntu/sfxlcl3?sid=metalib:ISI_WOS_XML&id=doi:&genre=&isbn=&issn=1064-8275&date=2003&volume=25&issue=3&spage=881&epage=904&aulast=Chan&aufirst=%20TF&auinit=TF&title=SIAM%20JOURNAL%20ON%20SCIENTIFIC%20COMPUTING&atitle=Identification%20of%20discontinuous%20coefficients%20in%20elliptic%20problems%20using%20total%20variation%20regularization
dc.identifier.doi http://dx.doi.org/10.1137/S1064827599326020
dc.description.version Published version

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