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Memorias de investigación
Communications at congresses:
Topological derivatives for non-homogeneous inverse problems
Year:2007
Research Areas
  • Mathematics
Information
Abstract
In this work we deal with the reconstruction of buried objects in a Helmholtz transmission problem with non--constant coefficients. This type of problems arises in electromagnetic, thermal and acoustic settings. 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 analyzes homogeneous problems with different boundary conditions. We address here non--homogeneous materials, giving expressions for the topological derivatives by finding first the shape derivative of the associated cost functional and then carrying out asymptotic expansions of the solutions of Helmholtz transmission problems in domains with vanishing holes. An efficient numerical scheme to compute the topological derivative is presented. Finally, we test the accuracy of the method for some different geometries in the two dimensional setting. We will see that the simple calculation of the topological derivative provides good initial guesses of the number of obstacles and their shape for a fast iterative method based on topological derivatives that allows for very accurate reconstructions.
International
Si
Congress
ENUMATH 2007
960
Place
Graz (Austria)
Reviewers
Si
ISBN/ISSN
Start Date
10/09/2007
End Date
14/09/2007
From page
To page
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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