Stable Phase Field Methods: Freeing the Dynamics from the Tyranny of the Lattice
Benjamin P. Vollmayr-Lee (Department of Physics & Astronomy, Bucknell University)

Phase field methods are widely used in modeling the dynamics and equilibrium properties of materials. Unfortunately, time marching the equations of motion generally requires keeping the time step below a fixed, lattice-dependent size in order to be numerically stable. Such stability-limited simulations are vastly less efficient than an accuracy-limited simulation could be, with a time step chosen by the natural time scale of the dynamics. I will review recent progress by Eyre and others in developing stable phase field methods. Then I will present a general approach for developing unconditionally stable steps (i.e. stable for any size time step) that consist of linear equations for the updated field. This allows for solution via fast Fourier transform, making the method simple and efficient. I will demonstrate the approach for the Allen-Cahn and Cahn-Hilliard equations, Swift-Hohenberg and phase field crystal models, an Ehrlich-Schwoebel type interface growth model, and the Ohta-Kawasaki model for block copolymers.