Recovery of multiple obstacles by probe method

Abstract

Abstract. We consider an inverse scattering problem for multiple obstacles D = N j=1 D j ⊂ R 3 with different types of boundary for D j . By constructing an indicator function from the far-field pattern of the scattered wave, we can firstly reconstruct the shape of all obstacles, then identify the type of boundary for each obstacle, as well as the boundary impedance in the case that obstacles have the Robin-type boundary condition. The novelty of our probe method compared with the existing probe method is that we succeeded in identifying the type of boundary condition for multiple obstacles by analyzing the behavior of both the imaginary part and the real part of the indicator function. The numerical realizations are given to show the performance of this inversion method.

Direct and Inverse Acoustic Scattering by a Combined Scatterer

“…In the same year, Ganesh and Hawkins in [11] generalized to the case of convex and non-convex multiple particles with different boundary condition and a few years later they developed a novel fast, high order, memory efficient algorithm to simulate multiple acoustic scattering induced by an ensemble with hundreds of particles in two space dimensions in [12]. In 2009, Cheng et al [7] made using of the probe method to identify multiple obstacles and the type of boundary conditions for each obstacle. In 2012, Challa, et al [5] have surveyed the direct and inverse electromagnetic scattering problem by a finite number of point-like obstacles.…”

The linear sampling method for a mixed scattering problem

“…In 2008, Ganesh and Hawkins [6] presented an algorithm for simulating acoustic scattering by multiple threedimensional sound-hard, sound-soft or absorbing impenetrable particles. In 2009, Cheng et al [7] considered an inverse scattering problem for multiple obstacles. In that paper, they firstly reconstructed the shape of all obstacles, then identified the type of boundary for each obstacle as well as the boundary impedance in the case that obstacles have the Robin-type boundary condition.…”

Recovering the Dirichlet-to-Neumann map in inverse scattering problems using integral equation methods

“…In this paper, we focus our attentions on the numerical implementations of D-to-N map for unknown D. To the authors' best knowledge, the present work is the first attempt to design an effective and accurate numerical method to compute the D-to-N map using the far-field measurements, although there are several numerical works on the initial probe method such as [2,3,6], where the authors directly test the probe method using synthetic D-to-N map obtained by solving the forward problem (1.4) as the input data. In this sense, our present work fills in this gap and provides a complete numerical scheme for the realization of the probe method by combining the early works in [2,3] with the computation of D-to-N map from far-field data.…”

“…In this sense, our present work fills in this gap and provides a complete numerical scheme for the realization of the probe method by combining the early works in [2,3] with the computation of D-to-N map from far-field data. In this process, the key point is to compute the derivatives of the scattered wave s (x, y) for point sources with respect to its two arguments from the far-field measurements corresponding to plane waves.…”