  In this paper, 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 Nystr\"om
method based on the curved quadratic elements, leading to simple numerical
implementation (no edge or corner problems) and high accuracy in the BEM
analysis. 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, resulting in two- to three-fold reduction in the
computational time of the multipole-to-local translations. 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 10 hours on a computer with one core and
the memory usage is 24 GB.
