  Fourier acceleration has been successfully applied to the simulation of
lattice field theories for more than a decade. In this paper, we extend the
method to the dynamics of discrete particles moving in continuum. Although our
method is based on a mapping of the particles' dynamics to a regular grid so
that discrete Fourier transforms may be taken, it should be emphasized that the
introduction of the grid is a purely algorithmic device and that no smoothing,
coarse-graining or mean-field approximations are made. The method thus can be
applied to the equations of motion of molecular dynamics (MD), or its Langevin
or Brownian variants. For example, in Langevin MD simulations our acceleration
technique permits a straightforward spectral decomposition of forces so that
the long-wavelength modes are integrated with a longer time step, thereby
reducing the time required to reach equilibrium or to decorrelate the system in
equilibrium. Speedup factors of up to 30 are observed relative to pure
(unaccelerated) Langevin MD. As with acceleration of critical lattice models,
even further gains relative to the unaccelerated method are expected for larger
systems. Preliminary results for Fourier-accelerated molecular dynamics are
presented in order to illustrate the basic concepts. Possible extensions of the
method and further lines of research are discussed.
