An Efficient Matrix-Free Finite Element Solver for the Cahn-Hilliard Equation

We focus on the efficient numerical solution of the mixed formulation of the Cahn–Hilliard equation. Themain challenges arise from the handling of an almost sharp moving phase boundary and processes on differenttime scales. We employ a higher order finite element method together with an adaptive time integrator. Inparticular, we use a fully parallelizable highly efficient matrix-free framework, which avoids the necessity of storing matrices.