  A highly efficient fast boundary element method (BEM) for solving large-scale
engineering acoustic problems in a broad frequency range is developed and
implemented. The acoustic problems are modeled by the Burton-Miller boundary
integral equation (BIE), thus the fictitious frequency issue is completely
avoided. The BIE is discretized by using the collocation method with piecewise
constant elements. The linear systems are solved iteratively and accelerated by
using a newly developed kernel-independent wideband fast directional algorithm
(FDA) for fast summation of oscillatory kernels. In addition, the computational
efficiency of the FDA is further promoted by exploiting the low-rank features
of the translation matrices. The high accuracy and nearly linear computational
complexity of the present method are clearly demonstrated by typical examples.
An acoustic scattering problem with dimensionless wave number $kD$ (where $k$
is the wave number and $D$ is the typical length of the obstacle) up to 1000
and the degrees of freedom up to 4 million is successfully solved within 4
hours on a computer with one core and the memory usage is 24.7 GB.
