Development and use of higher-order asymptotics to solve inverse scattering problems

Loading...
Thumbnail Image

Persistent link to this item

Statistics
View Statistics

Journal Title

Journal ISSN

Volume Title

Title

Development and use of higher-order asymptotics to solve inverse scattering problems

Published Date

2016-11

Publisher

Type

Thesis or Dissertation

Abstract

The purpose of this work was to develop new methods to address inverse problems in elasticity, taking advantage of the presence of a small parameter in the considered problems by means of higher-order asymptotic expansions. The first part is dedicated to the localization and size identification of a buried inhomogeneity B true in a 3D elastic domain. In this goal, we focus on the study of functionals J(Ba ) quantifying the misfit between Btrue and a trial homogeneity Ba . Such functionals are to be minimized w.r.t. some or all the characteristics of the trial inclusion Ba (location, size, mechanical properties ...) to find the best agreement with Btrue. To this end, we produce an expansion of J with respect to the size a of Ba , providing a polynomial approximation easier to minimize. This expansion is established in a volume integral equations framework up to the sixth order, and justified by an estimate of the residual. A suited identification procedure is then given and supported by numerical illustrations for simple obstacles in full-space R3. The main purpose of this second part is to characterize a microstructured two- phases layered 1D inclusion of length L, supposing we already know its low-frequency transmission eigenvalues (TEs). Those are computed as the eigenvalues of the so-called interior transmission problem (ITP). To provide a convenient invertible model, while accounting for the microstructure effects, we rely on homogenized approximations of the exact ITP for the periodic inclusion. Focusing on the leading-order homogenized ITP, we first provide a straightforward method to recover the macroscopic parameters (L and material contrast) of such inclusion. To access the key features of the microstructure, higher-order homogenization is finally addressed, with emphasis on the need for suitable boundary conditions.

Description

University of Minnesota Ph.D. dissertation. 2016. Major: Civil Engineering. Advisors: Bojan Guzina, Marc Bonnet. 1 computer file (PDF); 277 pages.

Related to

Replaces

License

Collections

Series/Report Number

Funding information

Isbn identifier

Doi identifier

Previously Published Citation

Suggested citation

Cornaggia, Remi. (2016). Development and use of higher-order asymptotics to solve inverse scattering problems. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/185191.

Content distributed via the University Digital Conservancy may be subject to additional license and use restrictions applied by the depositor. By using these files, users agree to the Terms of Use. Materials in the UDC may contain content that is disturbing and/or harmful. For more information, please see our statement on harmful content in digital repositories.