Numerical Integral Independent of Frequency in the Boundary Element Method for Acoustic Scattering

Abstract

Fast algorithm for multi-frequency numerical integration in the simulation of acoustic scattering from rigid object by the boundary element method is presented. Normal derivative of the free-space Greens function is partially approximated with the unknown variable by a set of shape functions. As a result, the numerical integral is independent of frequency and need be calculated only at the first frequency step. Singular integral can be computed using the same procedure as that applied in the conventional boundary element method. Computational efficiency and accuracy of the new technique are demonstrated by an example. Numerical results obtained using the new technique are compared with the corresponding analytical solutions and numerical results obtained using the conventional boundary element method. The new technique works well and saves a lot of computational time in the process of generation of coefficient matrices for multi-frequency analysis.