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Inverse Problems and Imaging (IPI)
 

A quasi-reversibility approach to solve the inverse obstacle problem

Pages: 351 - 377, Volume 4, Issue 3, August 2010      doi:10.3934/ipi.2010.4.351

 
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Laurent Bourgeois - Laboratoire POEMS, ENSTA, 32, Boulevard Victor, 75739 Paris Cedex 15, France (email)
Jérémi Dardé - Laboratoire POEMS, ENSTA, 32, Boulevard Victor, 75739 Paris Cedex 15, France (email)

Abstract: We introduce a new approach based on the coupling of the method of quasi-reversibility and a simple level set method in order to solve the inverse obstacle problem with Dirichlet boundary condition. We provide a theoretical justification of our approach and illustrate its feasibility with the help of numerical experiments in $2D$.

Keywords:  inverse obstacle problem, method of quasi-reversibility, level set method.
Mathematics Subject Classification:  35A15, 35N25, 35R25, 35R30,35R35, 65M60.

Received: May 2009;      Revised: November 2009;      Available Online: July 2010.