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Memorias de investigación
Research Publications in journals:
Solving inhomogeneous inverse problems by topological derivative methods
Year:2008
Research Areas
  • Mathematics
Information
Abstract
We introduce new iterative schemes to reconstruct scatterers buried in amedium and their physical properties. The inverse scattering problem is reformulated as a constrained optimization problem involving transmission boundary value problems in heterogeneous media. Our first step consists in developing a reconstruction scheme assuming that the properties of the objects are known. In a second step, we combine iterations to reconstruct the objects with iterations to recover the material parameters. This hybrid method provides reasonable guesses of the parameter values and the number of scatterers, their location and size. Our schemes to reconstruct objects knowing their nature rely on an extended notion of topological derivative. Explicit expressions for the topological derivatives of the corresponding shape functionals are computed in general exterior domains. Small objects, shapes with cavities and poorly illuminated obstacles are easily recovered. To improve the predictions of the parameters in the successive guesses of the domains we use a gradient method.
International
Si
JCR
Si
Title
INVERSE PROBLEMS
ISBN
0266-5611
Impact factor JCR
1,854
Impact info
Volume
4
Journal number
0
From page
1
To page
34
Month
ENERO
Ranking
Participants
  • Autor: Ana Carpio (Universidad Complutense de Madrid)
  • Autor: Maria Luisa Rapun Banzo (UPM)
Research Group, Departaments and Institutes related
  • Creador: Grupo de Investigación: Dinámica y estabilidad no lineal en ingeniería aeroespacial
  • Departamento: Fundamentos Matemáticos de la Tecnología Aeronáutica
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