An efficient Semi-Implicit Fourier-Spectral method is implemented to
solve the Cahn-Hilliard equation with a variable mobility.  The method
is orders of magnitude more efficient than the conventional forward
Euler finite-difference method, thus allowing us to simulate large
systems for longer times.  We studied the coarsening kinetics of
interconnected two-phase mixtures using a Cahn-Hilliard equation with
its mobility depending on local compositions.  In particular, we
compared the kinetics of bulk-diffusion- and
interface-diffusion-dominated coarsening in two-phase systems.
Results are compared with existing theories and previous computer
simulations.