We present a nonlinear multigrid implementation for the two-dimensional
Cahn–Hilliard (CH) equation. The CH equation was originally developed by
Cahn and Hilliard to model phase separation phenomenon. The CH equa-
tion has been used to model many interface-related problems such as spin-
odal decomposition of a binary alloy mixture, inpainting of binary images,
microphase separation of diblock copolymers, microstructures with elastic
inhomogeneity, two-phase binary fluids, in silico tumor growth simulation,
and structural topology optimization. The CH equation is discretized by
using Eyre’s unconditionally gradient stable scheme. The system of discrete
equations is solved using an iterative method such as a nonlinear multigrid
approach, which is one of the most efficient iterative methods for solving par-
tial differential equations. Characteristic numerical experiments are given to
show the efficiency and accuracy of the multigrid method for the CH equa-
tion.