Topological derivative based methods for non-destructive testing



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Carpio, Ana and Rapún, M.L. (2008) Topological derivative based methods for non-destructive testing. In Numerical mathematics and advanced applications. Springer, Berlin, pp. 687-694. ISBN 978-3-540-69776-3

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We propose a numerical strategy to reconstruct scatterers buried in a medium when the incident radiation (electromagnetic, thermal, acoustic) is governed by Helmholtz transmission problems. The scattering problem is recast as a shape optimization problem with the Helmholtz equation as a constraint and the scatterer as a design variable. Our method is based on the (successive) computation of topological derivatives of the associated shape functional for updated guesses of the scatterer.
We present an efficient scheme to compute the required topological derivatives at each step. The scheme combines explicit expressions for the topological derivatives in terms of the solutions of forward and adjoint transmission problems with boundary elementfinite element approximations. Our technique applies in either spatially homogeneous or inhomogeneous media. Finally, a two dimensional numerical test illustrates the ability of the method to reconstruct buried shapes

Item Type:Book Section
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Proceedings of ENUMATH 2007, the 7th European conference on numerical mathematics and advanced applications, Graz, Austria, September 10–14, 2007

Uncontrolled Keywords:Numerical examples; non-destructive testing; Helmholtz transmission problems; scattering; Helmholtz equation; topological derivatives
Subjects:Sciences > Mathematics > Numerical analysis
ID Code:15244
Deposited On:17 May 2012 07:55
Last Modified:04 Sep 2020 08:48

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