Efficient Finite Difference Methods for Acoustic Scattering from Circular Cylindrical Obstacle

Abstract

We consider efficient finite difference methods for solving the three-dimensional (3D) acoustic scattering by an impenetrable circular cylindrical obstacle. By using the separation of variable and other techniques, we first transform the 3D problem into a series of one-dimensional (1D) problems in this paper, and then construct some efficient and accuracy finite difference methods to solve these 1D problems instead of the 3D one. There are mainly two advantages for these methods: one is that they are pollution free for the problem to be considered in this paper; and the other is that the linear systems generated from these schemes have tri-diagonal structures. These features lead to easy implementation and much less computational cost. Numerical examples are presented to verify the efficiency and accuracy of the numerical methods, even with the wave number greater than 100.