A quasi-reversibility approach to solve the inverse obstacle problem

Laurent Bourgeois (1) , Jérémi Dardé (1, 2)

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
2 LJLL - Laboratoire Jacques-Louis Lions

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. © 2010 American Institute of Mathematical Sciences.

Mots clés: inverse obstacle problem; method of quasi-reversibility; level set method

Domaines: Analyse numérique [math.NA]

Laurent Bourgeois, Jérémi Dardé. A quasi-reversibility approach to solve the inverse obstacle problem. Inverse Problems and Imaging , 2010, 4 (3), pp.351-377. ⟨10.3934/ipi.2010.4.351⟩. ⟨hal-00873059⟩