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Domain reconstruction using photothermal techniques



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Carpio, Ana y Rapún, M.L. (2008) Domain reconstruction using photothermal techniques. Journal of Computational Physics, 227 (17). pp. 8083-8106. ISSN 0021-9991

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URL Oficial: http://www.sciencedirect.com/science/journal/00219991

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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.

Tipo de documento:Artículo
Palabras clave:Shape reconstruction; Nondestructive testing; Topological derivatives; Laplace transform; Boundary integral methods; Scattering; Heat equation; Thermal waves
Materias:Ciencias > Física > Física matemática
Ciencias > Matemáticas > Análisis numérico
Código ID:14930
Depositado:20 Abr 2012 11:28
Última Modificación:28 Oct 2016 08:04

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