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Topological Derivatives for Shape Reconstruction

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Carpio, Ana y Rapún, M.L. (2008) Topological Derivatives for Shape Reconstruction. Inverse problems and imaging, 1943 . pp. 85-133. ISSN 0075-8434

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URL Oficial: http://www.springerlink.com/content/q47k22718j526414/fulltext.pdf


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Resumen

Topological derivative methods are used to solve constrained optimization reformulations of inverse scattering problems. The constraints take the form of
Helmholtz or elasticity problems with different boundary conditions at the interface between the surrounding medium and the scatterers. Formulae for the topological derivatives are found by first computing shape derivatives and then performing suitable asymptotic expansions in domains with vanishing holes. We discuss integral methods for the numerical approximation of the scatterers using topological derivatives and implement a fast iterative procedure to improve the description of their number, size, location and shape.


Tipo de documento:Artículo
Palabras clave:Inverse obstacle scattering; Boundary inegral-equations; Level set methods; Transmission problems; Helmholtz-equation; Anisotropic elasticity; Sampling method; Tomography; Waves; Optimization
Materias:Ciencias > Matemáticas > Ecuaciones diferenciales
Código ID:14944
Depositado:24 Abr 2012 10:51
Última Modificación:28 Oct 2016 08:31

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