  Slow dynamics in disordered materials prohibits direct simulation of their
rich nonequilibrium behavior at large scales. "Patchwork dynamics" is
introduced to mimic relaxation over a very broad range of time scales by
equilibrating or optimizing directly on successive length scales. This dynamics
is used to study coarsening and to replicate memory effects for spin glasses
and random ferromagnets. It is also used to find, with high confidence, exact
ground states in large or toroidal samples.
