Observatorio de I+D+i UPM

Memorias de investigación
Topological derivatives for shape and parameter reconstruction
Áreas de investigación
  • Ingeniería aeronaútica
Numerical methods based on the computation of topological derivatives are very powerful tools for inverse scattering problems associated with shape reconstruction and non¿destructive 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.
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Entidad relacionada
Sociedad Española de Matemática Aplicada
Nacionalidad Entidad
Lugar del congreso
A Coruña
Esta actividad pertenece a memorias de investigación
  • Autor: Maria Luisa Rapun Banzo (UPM)
  • Participante: Ana Carpio (Universidad Complutense de Madrid)
Grupos de investigación, Departamentos, Centros e Institutos de I+D+i relacionados
  • Creador: Grupo de Investigación: Dinámica y estabilidad no lineal en ingeniería aeroespacial
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