Abstract.
   An effcient and high-order algorithm for
   three-dimensional bounded obstacle scattering is developed. The
   method is a non-trivial extension of recent work of the authors for
   two-dimensional bounded obstacle scattering, and is based on a
   boundary perturbation technique coupled to a well-conditioned
   high-order spectral-Galerkin solver. This boundary perturbation
   approach is justified by rigorous theoretical results on
   analyticity of the scattered field with respect to boundary
   variations which show that, in fact, the domain of analyticity can
   be extended to a neighborhood of the entire real axis. The 
   numerical method is augmented by Pade approximation techniques to
   access this region of extended analyticity so that
   configurations which are large deformations of the base
   (spherical) geometry can be simulated. Several numerical results
   are presented to exemplify the accuracy, stability, and versatility
   of the proposed method.