RT Journal Article
T1 Domain reconstruction using photothermal techniques
A1 Carpio Rodríguez, Ana María
A1 Rapún Banzo, María Luisa
AB A numerical method to detect objects buried in a medium by surface thermal measurements is presented. We propose a new approach combining the use of topological derivatives and Laplace transforms. The original optimization problem with time-dependent constraints is replaced by an equivalent problem with stationary constraints by means of Laplace transforms. The first step in the reconstruction scheme consists in discretizing the inversion formula to produce an approximate optimization problem with a finite set of constraints. Then, an explicit expression for the topological derivative of the approximate shape functional is given. This formula is evaluated at low cost using explicit expressions of the forward and adjoint fields involved. We apply this technique to a simple shape reconstruction problem set in a half space. Good approximations of the number, location and size of the obstacles are obtained. The description of their shapes can be improved by more expensive hybrid methods combining time averaging with topological derivative based iterative schemes.
PB Elsevier
SN 0021-9991
YR 2008
FD 2008
LK https://hdl.handle.net/20.500.14352/49853
UL https://hdl.handle.net/20.500.14352/49853
LA eng
NO Carpio Rodríguez, A. M. y Rapún Banzo, M. L. «Domain Reconstruction Using Photothermal Techniques». Journal of Computational Physics, vol. 227, n.o 17, septiembre de 2008, pp. 8083-106. DOI.org (Crossref), https://doi.org/10.1016/j.jcp.2008.05.014.
NO Ministerio de Educación, Formación Profesional y Deportes (España)
NO Fondo Europeo de Desarrollo Regional
DS Docta Complutense
RD 6 abr 2025