A Numerical Study of the Probe Method

Recovery of multiple obstacles by probe method

“…Then we can solve this problem by potential theory to generate the Neumann data on ∂Ω. The details for this procedure in the one-obstacle case may be found in [2,8,21].…”

“…We present the scheme for the reconstructions of multiple obstacles based on the scheme given in [8]. Although the theoretical analysis only gives the behavior of the indicator function I(t, c) given by (3.3) when c(t) approaches the boundaries of the obstacles from the outside, we compute I n (t, c) for fixed n 1 and all c(t).…”

“…For this, we use the scheme proposed in [8] which is as follows. To start with, we consider the minimum norm solution of the equation…”

“…For simplicity, we present the realizations of the probe method for multiple obstacles in R 2 . The numerical realization of the probe method was first given in [8] for one sound-soft obstacle and later given in [2] for one obstacle with impedance boundary.…”

“…The numerical performance of our method for the two dimensional case was tested for 3 circle shaped obstacles with different types of boundaries using the numerical realization scheme of the probe method given in [8]. The numerical result shows that we can reconstruct a little more than a convex hull of multiple obstacles only; the neighboring parts of different obstacles are hard to recover.…”