High-frequency scattering from convex and non-convex bodies is studied using an iterative algorithm. The key point of the method is a self-adjoint formulation of the Helmholtz integral equation, which ensures the convergence of the iteration process toward the true solution. For all investigated structures with different surface impedances fast convergence could be observed. The number of surface elements of the scatterer varies from about 6000 to 60 000 and the calculations are performed in the high-frequency range with Helmholtz numberskabetween 20 and 63. Even for a scattering structure with nearly 60 000 boundary elements, all computations could be carried out on a regular personal computer.