Kress, RainerSerranho, Pedro2011-10-312011-10-312007Kress, Rainer; Serranho, Pedro - A hybrid method for sound-hard obstacle reconstruction. "Journal of Computational and Applied Mathematics" [Em linha]. ISSN 0377-0427. Vol. 204, nº 2 (Jul. 2007), p. 1-130377-0427http://hdl.handle.net/10400.2/1931We are interested in solving the inverse problem of acoustic wave scattering to reconstruct the position and the shape of sound-hard 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 sound-soft cracks as presented in [R. Kress, P. Serranho, A hybrid method for two-dimensional crack reconstruction, Inverse Problems 21 (2005) 773–784] to the case of sound-hard 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. 93–102. 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.engInverse scattering problemHybrid methodNeumann boundary conditionjournal article