A simple and efficient scheme for phase field crystal simulation

Matt Elsey, Benedikt Wirth
2013 Mathematical Modelling and Numerical Analysis  
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
more » ... ted stability and error analysis as well as numerical experiments to validate the method's efficiency.
doi:10.1051/m2an/2013074 fatcat:z272pttlsfgplpqhtkmwmrdw5m