  An efficient solver for the three dimensional free-space Poisson equation is
presented. The underlying numerical method is based on finite Fourier series
approximation. While the error of all involved approximations can be fully
controlled, the overall computation error is driven by the convergence of the
finite Fourier series of the density. For smooth and fast-decaying densities
the proposed method will be spectral accurate. The method scales with
$\mathcal{O}(N\log N)$ operations, where $N$ is the total number of
discretization points in the Cartesian grid. The majority of the computational
costs come from fast Fourier transforms (FFT), which makes it ideal for GPU
computation. Several numerical computations on CPU and GPU validate the method
and show efficiency and convergence behavior. Tests are performed using the
Vienna Scientific Cluster 3 (VSC3). A free MATLAB implementation for CPU and
GPU is provided to the interested community.
