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 BEM–FEM 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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Carpio, A., Rapún, M.–. (2008). Topological Derivative Based Methods for Non–lDestructive Testing. In: Kunisch, K., Of, G., Steinbach, O. (eds) Numerical Mathematics and Advanced Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69777-0_82
Download citation
DOI: https://doi.org/10.1007/978-3-540-69777-0_82
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69776-3
Online ISBN: 978-3-540-69777-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)