In this paper we develop an iterative method to perform single and multiple scattering analyses of both convex and non-convex scatterers at very low computational cost and time. The computational method proposed will resolve the current inaccuracy of the On Surface Radiation Conditions (OSRC) in estimating the scattered field from non-convex obstacles and allows a fast and reliable single- and multiple-scattering analyses in reduced spatial dimensions. We demonstrate the reliability and efficiency of the proposed method in solving two- and three-dimensional time-harmonic acoustic scattering problems. Non-Uniform Rational B-Splines were used to represent the obstacle boundaries providing a seamless connection to geometrical representation. The proposed Iterative On Surface Radiation Conditions (ITOSRC) method tremendously reduces the meshing and analysis time and paves the way for shape and topology optimization of future devices relying on wave prpagation phenomena.