Some Efficient Precoditioners for the Semi-implicit Systems of the Cahn-Hilliard Equation

This paper studies efficient preconditioners for the discrete system of the Cahn-Hilliard equation which describes a phase separation phenomenon. The commonly used discrete scheme, for example, implicit or semi-implicit schemes need to solve lots of large saddle point linear systems. The main objective of this work is to construct some efficient preconditioners for the semi-implicit schemes of the Cahn-Hilliard equation. The preconditioners we constructed are uniform and easy to implement by multi-grid method. Numerical results show the preconditioners combined with Gmres are optimal for the Cahn-Hilliard equation.