Observatorio de I+D+i UPM

Memorias de investigación
Variational methods for inverse scattering problems
Research Areas
  • Aeronautical engineering
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. 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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Universidad de Birmingham
Entity Nationality
  • Autor: Maria Luisa Rapun Banzo (UPM)
  • Participante: Ana Carpio (Universidad Complutense de Madrid)
Research Group, Departaments and Institutes related
  • Creador: Grupo de Investigación: Dinámica y estabilidad no lineal en ingeniería aeroespacial
S2i 2021 Observatorio de investigación @ UPM con la colaboración del Consejo Social UPM
Cofinanciación del MINECO en el marco del Programa INNCIDE 2011 (OTR-2011-0236)
Cofinanciación del MINECO en el marco del Programa INNPACTO (IPT-020000-2010-22)