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

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    Author
    Beretta, Elena; de Hoop, Maarten V.; Faucher, Florian; Scherzer, Otmar
    Date
    2016
    Abstract
    We 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.
    Citation
    Beretta, Elena, de Hoop, Maarten V., Faucher, Florian, et al.. "Inverse Boundary Value Problem For The Helmholtz Equation: Quantitative Conditional Lipschitz Stability Estimates." SIAM Journal on Mathematical Analysis, 48, no. 6 (2016) SIAM: 3962-3983. http://dx.doi.org/10.1137/15M1043856.
    Published Version
    http://dx.doi.org/10.1137/15M1043856
    Type
    Journal article
    Publisher
    SIAM
    Citable link to this page
    https://hdl.handle.net/1911/94277
    Rights
    Article 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.
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    Home | FAQ | Contact Us | Privacy Notice | Accessibility Statement
    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
    Mailing Address: MS-44, P.O.BOX 1892, Houston, Texas 77251-1892
    Site Map