A multigrid solution for the Cahn-Hilliard equation on nonuniform grids

The existence of global attractor for a Cahn-Hilliard/Allen-Cahn‎ ‎equation

In this paper, we consider a Cahn-Hillard/Allen-Cahn equation. By using the semigroup and the classical existence theorem of global attractors, we give the existence of the global attractor in H^k(0

Three-dimensional volume reconstruction from slice data using phase-field models

We propose the application of a phase-field framework for three-dimensional volume reconstruction using slice data. The proposed method is based on the Allen–Cahn and Cahn–Hilliard equations, and the algorithm consists of two steps. First, we perform image segmentation on the given raw data using a modified Allen– Cahn equation. Second, we reconstruct a three-dimensional volume using amodified ...

An H Convergence of a Second-order Convex-splitting, Finite Difference Scheme for the Three-dimensional Cahn–hilliard Equation∗

In this paper we present an unconditionally solvable and energy stable second order numerical scheme for the three-dimensional (3D) Cahn–Hilliard (CH) equation. The scheme is a twostep method based on a second order convex splitting of the physical energy, combined with a centered difference in space. The equation at the implicit time level is nonlinear but represents the gradients of a strictl...

A multigrid method for the Cahn-Hilliard equation with obstacle potential

Numerical and computational efficiency of solvers for two-phase problems

We consider two-phase flow problems, modelled by the Cahn-Hilliard equation. In our work, the nonlinear fourth-order equation is decomposed into a system of two second-order equations for the concentration and the chemical potential. We analyse solution methods based on an approximate two-by-two block factorization of the Jacobian of the nonlinear discrete problem. We propose a preconditioning ...