Computations on the Cahn-Hilliard model of solidification

摘要

We begin numerical studies of interface migration on the two-dimensional Cahn-Hilliard equation. Our results add evidence to support the connection between this equation and the well-known quasistatic model of solidification. Finite elements coupled with a second-order time discretization scheme are used. The nonlinear systems of equations that arise on each time step are solved by fixed-point iteration, while the linear systems are solved by preconditioned conjugate gradients.