  This paper is devoted to the efficient numerical solution of the Helmholtz
equation in a two- or three-dimensional rectangular domain with an absorbing
boundary condition (ABC). The Helmholtz problem is discretized by standard
bilinear and trilinear finite elements on an orthogonal mesh yielding a
separable system of linear equations. The main key to high performance is to
employ the Fast Fourier transform (FFT) within a fast direct solver to solve
the large separable systems. The computational complexity of the proposed FFT
based direct solver is O(N log N) operations. Numerical results for both two-
and three-dimensional problems are presented confirming the efficiency of the
method discussed.
