2026-06-29T03:08:25Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/531082024-07-10T13:14:13Zcom_20.500.14352_14col_20.500.14352_21

Carpio Rodríguez, Ana María Rapún Banzo, María Luisa 2023-06-20T13:38:01Z 2023-06-20T13:38:01Z 2008 978-3-540-69776-3 https://hdl.handle.net/20.500.14352/53108 http://www.springerlink.com/content/q255677657446681/ 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 eng restricted access Topological derivative based methods for non-destructive testing book part