# Science at the triple point between mathematics, mechanics and materials science

## Publication 25

### A simple and efficient scheme for phase field crystal simulation

##### Authors:

Matt Elsey
Courant Institute of Mathematical Sciences
New York University

Benedikt Wirth

##### Abstract:
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.
##### Get the paper in its entirety
StableandeffElsey.pdf

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