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

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Development and use of higher-order asymptotics to solve inverse scattering problems./
Author:	Cornaggia, Remi.
Description:	1 online resource (277 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-07(E), Section: B.
Contained By:	Dissertation Abstracts International78-07B(E).
Subject:	Applied mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781369601756

Development and use of higher-order asymptotics to solve inverse scattering problems.
Cornaggia, Remi.

Development and use of higher-order asymptotics to solve inverse scattering problems. - 1 online resource (277 pages)

Source: Dissertation Abstracts International, Volume: 78-07(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

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.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369601756Subjects--Topical Terms:

1069907
Applied mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Development and use of higher-order asymptotics to solve inverse scattering problems.
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020 $a 9781369601756
035 $a (MiAaPQ)AAI10245469
035 $a (MiAaPQ)umn:17731
035 $a AAI10245469
040 $a MiAaPQ $b eng $c MiAaPQ
099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Cornaggia, Remi. $3 1180557
245 1 0 $a Development and use of higher-order asymptotics to solve inverse scattering problems.
264 0 $c 2016
300 $a 1 online resource (277 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-07(E), Section: B.
500 $a Advisers: Bojan B. Guzina; Marc Bonnet.
502 $a Thesis (Ph.D.) $c University of Minnesota $d 2016.
504 $a Includes bibliographical references
520 $a 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.
520 $a The first part is dedicated to the localization and size identification of a buried inhomogeneity Btrue in a 3D elastic domain. In this goal, we focus on the study of functionals J( Ba ) quantifying the misfit between B true 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 B true. 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.
520 $a 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.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Applied mathematics. $3 1069907
650 4 $a Civil engineering. $3 561339
655 7 $a Electronic books. $2 local $3 554714
690 $a 0364
690 $a 0543
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of Minnesota. $b Civil Engineering. $3 1179810
773 0 $t Dissertation Abstracts International $g 78-07B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10245469 $z click for full text (PQDT)