A hybrid method for soundhard obstacle reconstruction
Abstract
We are interested in solving the inverse problem of acoustic wave scattering to reconstruct the position and the shape of soundhard obstacles from a given incident field and the corresponding far field pattern of the scattered field. The method we suggest is an extension of the hybrid method for the reconstruction of soundsoft cracks as presented in [R. Kress, P. Serranho, A hybrid method for twodimensional crack reconstruction, Inverse Problems 21 (2005) 773784] to the case of soundhard obstacles. The designation of the method is justified by the fact that it can be interpreted as a hybrid between a regularized Newton method applied to a nonlinear operator equation with the operator that maps the unknown boundary onto the solution of the direct scattering problem and a decomposition method in the spirit of the potential method as described in [A. Kirsch, R. Kress, On an integral equation of the first kind in inverse acoustic scattering, in: Cannon, Hornung (Eds.), Inverse Problems, ISNM, vol. 77, 1986, pp. 93102. Since the method does not require a forward solver for each Newton step its computational costs are reduced. By some numerical examples we illustrate the feasibility of the method.
 Publication:

Journal of Computational and Applied Mathematics
 Pub Date:
 July 2007
 Bibcode:
 2007JCoAM.204..418K
 Keywords:

 Inverse scattering problems