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Stabilized variational formulation f...

Babaniyi, Olalekan Adeoye.

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

Record Type:	Electronic resources : Monograph/item
Title/Author:	Stabilized variational formulation for direct solution of inverse problems in heat conduction and elasticity with discontinuities./
Author:	Babaniyi, Olalekan Adeoye.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2016,
Description:	134 p.
Notes:	Source: Dissertation Abstracts International, Volume: 77-07(E), Section: B.
Contained By:	Dissertation Abstracts International77-07B(E).
Subject:	Mechanical engineering. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10017004
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. - Ann Arbor : ProQuest Dissertations & Theses, 2016 - 134 p.

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

Thesis (Ph.D.)--Boston University, 2016.

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.

ISBN: 9781339499475Subjects--Topical Terms:

649730
Mechanical engineering.

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 3342783
245 1 0 $a Stabilized variational formulation for direct solution of inverse problems in heat conduction and elasticity with discontinuities.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2016
300 $a 134 p.
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.)--Boston University, 2016.
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.
590 $a School code: 0017.
650 4 $a Mechanical engineering. $3 649730
650 4 $a Mechanics. $3 525881
650 4 $a Medical imaging. $3 3172799
690 $a 0548
690 $a 0346
690 $a 0574
710 2 $a Boston University. $b Mechanical Engineering. $3 3181610
773 0 $t Dissertation Abstracts International $g 77-07B(E).
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791 $a Ph.D.
792 $a 2016
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10017004