We propose an unconditionally stable semi-implicit time discretization of the phase field
crystal evolution. It is based on splitting the underlying energy into convex and concave
parts and then performing H-1 gradient descent steps implicitly for the former
and explicitly for the latter. The splitting is effected in such a way that the resulting
equations are linear in each time step and allow an extremely simple implementation and
efficient solution. We provide the associated stability and error analysis as well as
numerical experiments to validate the method’s efficiency.