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Stabilized variational formulation for direct solution of inverse problems in heat conduction and elasticity with discontinuities.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Stabilized variational formulation for direct solution of inverse problems in heat conduction and elasticity with discontinuities./
Author:	Babaniyi, Olalekan Adeoye.
Description:	1 online resource (134 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 77-07(E), Section: B.
Contained By:	Dissertation Abstracts International77-07B(E).
Subject:	Mechanical engineering. -
Online resource:	click for full text (PQDT)
ISBN:	9781339499475

Stabilized variational formulation for direct solution of inverse problems in heat conduction and elasticity with discontinuities.
Babaniyi, Olalekan Adeoye.

Stabilized variational formulation for direct solution of inverse problems in heat conduction and elasticity with discontinuities. - 1 online resource (134 pages)

Source: Dissertation Abstracts International, Volume: 77-07(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

We consider the design of finite element methods for inverse problems with full-field data governed by elliptic forward operators. Such problems arise in applications in inverse heat conduction, in mechanical property characterization, and in medical imaging. For this class of problems, novel finite element methods have been proposed (Barbone et al., 2010) that give good performance, provided the solutions are in the H1(O) function space. The material property distributions being estimated can be discontinuous, however, and therefore it is desirable to have formulations that can accommodate discontinuities in both data and solution. Toward this end, we present a mixed variational formulation for this class of problems that handles discontinuities well. We motivate the mixed formulation by examining the possibility of discretizing using a discontinuous discretization in an irreducible finite element method, and discuss the limitations of that approach. We then derive a new mixed formulation based on a least-square error in the constitutive equation. We prove that the continuous variational formulations are well-posed for applications in both inverse heat conduction and plane stress elasticity. We derive a priori error bounds for discretization error, valid in the limit of mesh refinement. We demonstrate convergence of the method with mesh refinement in cases with both continuous and discontinuous solutions. Finally we apply the formulation to measured data to estimate the elastic shear modulus distributions in both tissue mimicking phantoms and in breast masses from data collected in vivo.

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

Mode of access: World Wide Web

ISBN: 9781339499475Subjects--Topical Terms:

557493
Mechanical engineering.
Index Terms--Genre/Form:

554714
Electronic books.

Stabilized variational formulation for direct solution of inverse problems in heat conduction and elasticity with discontinuities.
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100 1 $a Babaniyi, Olalekan Adeoye. $3 1180166
245 1 0 $a Stabilized variational formulation for direct solution of inverse problems in heat conduction and elasticity with discontinuities.
264 0 $c 2016
300 $a 1 online resource (134 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
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500 $a Source: Dissertation Abstracts International, Volume: 77-07(E), Section: B.
500 $a Advisers: Paul E. Barbone; Assad A. Oberai.
502 $a Thesis (Ph.D.) $c Boston University $d 2016.
504 $a Includes bibliographical references
520 $a We consider the design of finite element methods for inverse problems with full-field data governed by elliptic forward operators. Such problems arise in applications in inverse heat conduction, in mechanical property characterization, and in medical imaging. For this class of problems, novel finite element methods have been proposed (Barbone et al., 2010) that give good performance, provided the solutions are in the H1(O) function space. The material property distributions being estimated can be discontinuous, however, and therefore it is desirable to have formulations that can accommodate discontinuities in both data and solution. Toward this end, we present a mixed variational formulation for this class of problems that handles discontinuities well. We motivate the mixed formulation by examining the possibility of discretizing using a discontinuous discretization in an irreducible finite element method, and discuss the limitations of that approach. We then derive a new mixed formulation based on a least-square error in the constitutive equation. We prove that the continuous variational formulations are well-posed for applications in both inverse heat conduction and plane stress elasticity. We derive a priori error bounds for discretization error, valid in the limit of mesh refinement. We demonstrate convergence of the method with mesh refinement in cases with both continuous and discontinuous solutions. Finally we apply the formulation to measured data to estimate the elastic shear modulus distributions in both tissue mimicking phantoms and in breast masses from data collected in vivo.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mechanical engineering. $3 557493
650 4 $a Mechanics. $3 527684
650 4 $a Medical imaging. $3 1180167
655 7 $a Electronic books. $2 local $3 554714
690 $a 0548
690 $a 0346
690 $a 0574
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Boston University. $b Mechanical Engineering. $3 1148636
773 0 $t Dissertation Abstracts International $g 77-07B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10017004 $z click for full text (PQDT)