A new method for the parallelization of numerical methods for partial differential
equations (PDEs) in the temporal direction is presented. The method is
iterative with each iteration consisting of deferred correction sweeps performed
alternately on fine and coarse space-time discretizations. The coarse grid problems
are formulated using a space-time analog of the full approximation scheme
popular in multigrid methods for nonlinear equations. The current approach is
intended to provide an additional avenue for parallelization for PDE simulations
that are already saturated in the spatial dimensions. Numerical results and
timings on PDEs in one, two, and three space dimensions demonstrate the
potential for the approach to provide efficient parallelization in the temporal
direction.