Inverse Boundary Value Problem For The Helmholtz Equation: Quantitative Conditional Lipschitz Stability Estimates

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dc.citation.firstpage3962
dc.citation.issueNumber6
dc.citation.journalTitleSIAM Journal on Mathematical Analysis
dc.citation.lastpage3983
dc.citation.volumeNumber48
dc.contributor.authorBeretta, Elena
dc.contributor.authorde Hoop, Maarten V.
dc.contributor.authorFaucher, Florian
dc.contributor.authorScherzer, Otmar
dc.date.accessioned2017-05-15T21:11:38Z
dc.date.available2017-05-15T21:11:38Z
dc.date.issued2016
dc.description.abstractWe study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequencies as the data. A conditional Lipschitz stability estimate for the inverse problem holds in the case of wavespeeds that are a linear combination of piecewise constant functions (following a domain partition) and gives a framework in which the scheme converges. The stability constant grows exponentially as the number of subdomains in the domain partition increases. We establish an order optimal upper bound for the stability constant. We eventually realize computational experiments to demonstrate the stability constant evolution for three-dimensional wavespeed reconstruction.
dc.identifier.citationBeretta, Elena, de Hoop, Maarten V., Faucher, Florian, et al.. "Inverse Boundary Value Problem For The Helmholtz Equation: Quantitative Conditional Lipschitz Stability Estimates." <i>SIAM Journal on Mathematical Analysis,</i> 48, no. 6 (2016) SIAM: 3962-3983. http://dx.doi.org/10.1137/15M1043856.
dc.identifier.doihttp://dx.doi.org/10.1137/15M1043856
dc.identifier.urihttps://hdl.handle.net/1911/94277
dc.language.isoeng
dc.publisherSIAM
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
dc.titleInverse Boundary Value Problem For The Helmholtz Equation: Quantitative Conditional Lipschitz Stability Estimates
dc.typeJournal article
dc.type.dcmiText
dc.type.publicationpublisher version
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