On an optimisation method for the full- and the limited-aperture problem in inverse acoustic scattering for a sound-soft obstacle

A numerical method, developed by Kirsch and Kress (1988), for the determination of the shape of a two-dimensional time-harmonic acoustic scatterer with Dirichlet boundary conditions from the knowledge of the far-field pattern is considered. For the full-aperture problem with n incoming waves new convergence results are found. The corresponding computational part deals with the reduction of the computing time by a superposition of n incoming waves to a few 'total waves'. The method is extended to the limited-aperture problem; especially an estimation of its ill-posedness is given. Some numerical examples are presented with a measuring angle of 90 degrees and 180 degrees where it is shown that this method produces acceptable results for low wavenumbers.