## Maximally fast algorithm for Cahn-Hilliard equation

### March 18, 2007

Paper: Maximally fast coarsening algorithms

Authors: Mowei Cheng and Andrew D. Rutenberg

Abstract:

We present maximally fast numerical algorithms for conserved coarsening systems thatare stable and accurate with a growing natural time step $\Delta t = A t_{s}^{2/3}$. We compare the scaling structure obtained from our maximally fast conserved systems directly against the standard fixed time-step Euler algorithm, and find that the error scales as $\sqrt{A}$—so arbitrary accuracy can be achieved. For non-conserved systems, only effectively finite time steps are accessible for similar unconditionally stable algorithms.