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Cavity identification in linear elasticity and thermoelasticity

✍ Scribed by Hend Ben Ameur; Martin Burger; Benjamin Hackl

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
435 KB
Volume
30
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

The aim of this paper is an analysis of geometric inverse problems in linear elasticity and thermoelasticity related to the identification of cavities in two and three spatial dimensions. The overdetermined boundary data used for the reconstruction are the displacement and temperature on a part of the boundary.

We derive identifiability results and directional stability estimates, the latter using the concept of shape derivatives, whose form is known in elasticity and newly derived for thermoelasticity. For numerical reconstructions we use a least‐squares formulation and a geometric gradient descent based on the associated shape derivatives. The directional stability estimates guarantee the stability of the gradient descent approach, so that an iterative regularization is obtained. This iterative scheme is then regularized by a level set approach allowing the reconstruction of multiply connected shapes. Copyright © 2007 John Wiley & Sons, Ltd.

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