A meshless numerical identification of a sound-hard obstacle

We propose a simple meshless method for detecting a rigid (sound-hard) scatterer embedded in a host acoustic homogeneous medium from scant measurements of the scattered near field. This inverse problem is ill-posed since a solution may not be unique and furthermore, small errors in the input data cause large errors in the output solution. We develop a nonlinear minimization regularized method of fundamental solutions (MFS) for obtaining the numerical solution of the inverse problem in question. Although the MFS is restricted to homogeneous media with constant wavenumber, it is easy to use and simple to implement in higher dimensions. The proposed scheme is tested on several numerical examples and its stability is investigated by inverting measurements contaminated by random noise.