Topological derivatives for shape and parameter reconstruction

Carpio, Ana and Rapun Banzo, Maria Luisa (2010). Topological derivatives for shape and parameter reconstruction. In: "I Congreso Hispano Francés de Matemáticas", 09/07/2007 - 13/07/2007, Zaragoza, España.

Description

Title: Topological derivatives for shape and parameter reconstruction
Author/s:
  • Carpio, Ana
  • Rapun Banzo, Maria Luisa
Item Type: Presentation at Congress or Conference (Article)
Event Title: I Congreso Hispano Francés de Matemáticas
Event Dates: 09/07/2007 - 13/07/2007
Event Location: Zaragoza, España
Title of Book: Actas del I Congreso Hispano Francés de Matemáticas
Date: 2010
Subjects:
Faculty: E.T.S.I. Aeronáuticos (UPM)
Department: Fundamentos Matemáticos de la Tecnología Aeronáutica [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

Numerical methods based on the computation of topological derivatives are very powerful tools for inverse scattering problems associated with shape reconstruction and nondestructive testing. Recent work on topological derivatives focuses on problems where the nature of the scatterers is known [1¿4]. We address here the full problem, developing techniques to reconstruct objects buried in a medium and their physical properties. The medium and the objects are illuminated by an incident radiation (electromagnetic, thermal, acoustic). The total field, composed of incident, scattered and transmitted waves, satisfies a Helmholtz transmission problem in the plane. The inverse problem consists in reconstructing the objects and their material parameters from measurements of the total field at different locations. A weak reformulation as a constrained optimization problem is given. Our first step consists in developing a topological derivative based reconstruction scheme assuming that the properties of the objects are known. In a second step, we combine iterations to reconstruct the objects with gradient iterations to recover the material parameters. This strategy provides reasonable guesses of the parameter values, the number of scatterers, their location and size. Numerical experiments illustrate the accuracy of the method in different geometries.

More information

Item ID: 7590
DC Identifier: http://oa.upm.es/7590/
OAI Identifier: oai:oa.upm.es:7590
Official URL: http://www.unizar.es/ICHFM07/
Deposited by: Memoria Investigacion
Deposited on: 06 Jul 2011 12:02
Last Modified: 20 Apr 2016 16:41
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