Topological Derivative Based Methods for Non–lDestructive Testing

A. Carpio () and M. –L. Rapún ()
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A. Carpio: Universidad Complutense de Madrid, Dpto. Matemática Aplicada, Fac. Matemáticas
M. –L. Rapún: Universidad Politécnica de Madrid, Dpto. Fundamentos Matemáticos, E.T.S.I.Aeronáuticos

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 687-694 from Springer

Abstract: 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.

Keywords: Inverse Problem; Inverse Scattering; Forward Problem; Adjoint Problem; Shape Optimization Problem (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-69777-0_82

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DOI: 10.1007/978-3-540-69777-0_82

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