SIAM Journal on Numerical Analysis
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
Finite element approximation of the Cahn-Hilliard equation with concentration dependent mobility
Mathematics of Computation
Finite Element Approximation of the Cahn--Hilliard Equation with Degenerate Mobility
SIAM Journal on Numerical Analysis
Multigrid
A sharp interface Cartesian Ggid method for simulating flows with complex moving boundaries: 345
Journal of Computational Physics
Journal of Computational Physics
The Legendre collocation method for the Cahn-Hilliard equation
Journal of Computational and Applied Mathematics
Conservative multigrid methods for Cahn-Hilliard fluids
Journal of Computational Physics
A multigrid finite element solver for the Cahn-Hilliard equation
Journal of Computational Physics
A discontinuous Galerkin method for the Cahn-Hilliard equation
Journal of Computational Physics
On large time-stepping methods for the Cahn--Hilliard equation
Applied Numerical Mathematics
Local discontinuous Galerkin methods for the Cahn-Hilliard type equations
Journal of Computational Physics
A numerical method for the ternary Cahn--Hilliard system with a degenerate mobility
Applied Numerical Mathematics
Computers & Mathematics with Applications
Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models
Journal of Computational Physics
Hi-index | 31.46 |
We propose an efficient finite difference scheme for solving the Cahn-Hilliard equation with a variable mobility in complex domains. Our method employs a type of unconditionally gradient stable splitting discretization. We also extend the scheme to compute the Cahn-Hilliard equation in arbitrarily shaped domains. We prove the mass conservation property of the proposed discrete scheme for complex domains. The resulting discretized equations are solved using a multigrid method. Numerical simulations are presented to demonstrate that the proposed scheme can deal with complex geometries robustly. Furthermore, the multigrid efficiency is retained even if the embedded domain is present.