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A New Optimal Control Approach for the Reconstruction of Extended Inclusions
 

Summary: A New Optimal Control Approach for the Reconstruction
of Extended Inclusions
Habib Ammari
Pierre Garapon
Fran¸cois Jouve
Hyeonbae Kang§
Mikyoung Lim¶
Abstract
The aim of this paper is to propose a new optimal control formulation for recovering
an extended inclusion from boundary measurements. Our approach provides an optimal
representation of the shape of the inclusion. It guarantees local Lipschitz stability for
the reconstruction problem. Some numerical experiments are performed to demonstrate
the validity and the limitations of the proposed reconstruction method.
AMS subject classifications. 31B20, 35B37, 35L05
Key words. extended inclusion, reconstruction algorithm, optimal control, Helmholtz equation, shape
representation, MUSIC algorithm
1 Introduction and problem formulation
Let Rd
, d = 2, 3, be a bounded smooth simply connected domain. Let denote the
outward normal to the boundary . Suppose that contains an inclusion D away from

  

Source: Ammari, Habib - Centre de Mathématique Appliquées, École Polytechnique

 

Collections: Mathematics