The factorization method for a partially coated cavity in inverse scattering

Abstract

We consider the interior inverse scattering problem of recovering the shape of an impenetrable partially coated cavity. The scattered fields incited by point source waves are measured on a closed curve inside the cavity. We prove the validity of the factorization method for reconstructing the shape of the cavity. However, we are not able to apply the basic theorem introduced by Kirsch and Grinberg to treat the key operator directly, and some auxiliary operators have to be considered. In this paper, we provide theoretical validation of the factorization method to the problem, and some numerical results are presented to show the viability of our method.

Interior Elastic Scattering by a Non-Penetrable Partially Coated Obstacle and Its Shape Recovering

“…In what follows in this paper, we assume C be a Lipschitz closed curve inside B and B 0 be the interior domain enclosed by C. We also assume as incident wave a point-source u inc r 0 (r) given by u inc r 0 (r) ≡ Γ(r, r 0 ), r ∈ R 2 and r 0 ∈ C where Γ(r, r 0 ) is the fundamental Our scattering problem will be mathematically modelled by a mixed boundary value problem, and emphasis on its well-posedness using a variational method will be given. We will extend the results from the acoustic case proposed in [12] to the more complicated elastic one. We consider as incident elastic wave u inc r 0 , a source located at a point with position vector r 0 [13], i.e.,…”

“…with v = (v 1 , v 2 ) and w = (w 1 , w 2 ) is a specific energy functional in 2D-linear elasticity and expresses the energy disseminated through the point of the material being shifted. Using now Equation ( 9) and the notation ∂B ≡ Γ := Γ D ∪ Π ∪ Γ I , from (12) we take…”

“…We state the following lemma; its proof follows analogous arguments and minor modifications as those in [12,25], and here it is omitted for brevity. Lemma 1.…”

An approximate factorization method for inverse medium scattering with unknown buried objects

“…For the case = ∅ D 0 , the reader is referred to [4,11] for other qualitative methods such as the linear sampling method, the singular sources method and so on. For the factorization method for partially coated cavities and complex obstacles with generalized impedance boundary conditions, see [13,16].…”