Imaging from Internal Data
Imaging from Internal Data
This chapter introduces efficient methods for reconstructing both the shape and the elasticity parameters of an inclusion using internal displacement measurements. It first considers the inverse problem of recovering the shape and the (constant) shear modulus of an inclusion from internal measurements. The small-volume asymptotic framework is used to separate the information in the measurements into a near-field and a far-field part. A discrepancy function is then presented and a regularization is discussed. The chapter proceeds by describing the more general case of shear distributions, taking into account the discrepancy between the measured and computed displacement fields. In order to write down a descent gradient scheme in the case of a heterogeneous shear distribution, the derivative of the discrepancy function with respect to the shear modulus is computed.
Keywords: shape, elasticity, inclusion, internal displacement measurement, shear modulus, shear distribution, gradient scheme, heterogeneous shear distribution, discrepancy function
Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
Please, subscribe or login to access full text content.
If you think you should have access to this title, please contact your librarian.
To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.
