American Institute of Mathematical Sciences

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August  2010, 4(3): 351-377. doi: 10.3934/ipi.2010.4.351

A quasi-reversibility approach to solve the inverse obstacle problem

Laurent Bourgeois 1, and  Jérémi Dardé 1,

1. 

Laboratoire POEMS, ENSTA, 32, Boulevard Victor, 75739 Paris Cedex 15, France

Received  May 2009 Revised  November 2009 Published  July 2010

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, 65M6.
Citation: Laurent Bourgeois, Jérémi Dardé. A quasi-reversibility approach to solve the inverse obstacle problem. Inverse Problems & Imaging, 2010, 4 (3) : 351-377. doi: 10.3934/ipi.2010.4.351
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