  The spectral deferred correction (SDC) method is an iterative scheme for
computing a higher-order collocation solution to an ODE by performing a series
of correction sweeps using a low-order timestepping method. This paper examines
a variation of SDC for the temporal integration of PDEs called multi-level
spectral deferred corrections (MLSDC), where sweeps are performed on a
hierarchy of levels and an FAS correction term, as in nonlinear multigrid
methods, couples solutions on different levels. Three different strategies to
reduce the computational cost of correction sweeps on the coarser levels are
examined: reducing the degrees of freedom, reducing the order of the spatial
discretization, and reducing the accuracy when solving linear systems arising
in implicit temporal integration. Several numerical examples demonstrate the
effect of multi-level coarsening on the convergence and cost of SDC
integration. In particular, MLSDC can provide significant savings in compute
time compared to SDC for a three-dimensional problem.
