Cahn-Hilliard on Surfaces: A Numerical Study
For researchers simulating phase separation on surfaces (e.g., lipid membranes), this study provides a numerical method with convergence properties tied to spatial resolution, though it is an incremental contribution.
This work investigates a closest-point based numerical scheme for solving the Cahn-Hilliard system on surfaces, using an incomplete Schur-decomposition preconditioner. Results show that with high-order time discretization, the method's accuracy depends only on spatial resolution.
The Cahn-Hilliard system has been used to describe a wide number of phase separation processes, from co-polymer systems to lipid membranes. In this work the convergence properties of a closest-point based scheme is investigated. In place of solving the original fourth-order system directly, two coupled second-order systems are solved. The system is solved using an incomplete Schur-decomposition as a preconditioner. The results indicate that with a sufficiently high-order time discretization the method only depends on the underlying spatial resolution.