RT Book, Section
T1 Topological derivative based methods for non-destructive testing
A1 Carpio Rodríguez, Ana María
A1 Rapún Banzo, María Luisa
AB 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
PB Springer
SN 978-3-540-69776-3
YR 2008
FD 2008
LK https://hdl.handle.net/20.500.14352/53108
UL https://hdl.handle.net/20.500.14352/53108
LA eng
NO Proceedings of ENUMATH 2007, the 7th European conference on numerical mathematics and advanced applications, Graz, Austria, September 10–14, 2007
DS Docta Complutense
RD 17 abr 2025