Carpio Rodríguez, Ana María 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

Official URL: http://www.springerlink.com/content/q255677657446681/

## Abstract

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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Additional Information: | 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: | 17 May 2012 07:55 |

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