Abstract
The finite-difference approach based on the concept of the generalized scattering amplitude is extended to sound scatterings by three-dimensional obstacles. Numerical results for an example problem of scattering by a sphere are obtained for ka = 5, where k is the wave number equaling 2?r divided by the wavelength of the sound waves and a is the radius of the sphere. These results are in excellent agreement with those obtained by the eigenfunction expansion method. Results presented include spatial profiles of the generalized scattering amplitude, amplitude and phase of the total sound pressure, and bistatic scattering cross sections. The method shows promise for accurate, systematic calculations for bodies of arbitrary material, size, and shape. It is also applicable to classical scattering of electromagnetic waves and quantum scattering of particles.
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