Frequency-independent scattering for the large sphere

The high frequency scattering of a scalar plane wave from an impenetrable sphere with the diameter of one thousand wavelength is treated by the saddle-point technique and the numerical steepest descent method. The far-field solution for the sphere is computed in the observation angle range of 0 to 180 degree. In particular, a novel numerical steepest descent method is proposed to overcome the breakdown of the traditional saddle-point technique in the forward region. Numerical results show that the CPU time for the far-field calculation is frequency-independent with controllable error. This work can be used to benchmark future works in frequency-independent methods.