Unconditionally energy stable time stepping scheme for Cahn-Morral equation: Application to multi-component spinodal decomposition and optimal space tiling

An unconditionally energy stable time stepping scheme is introduced to solve CahnMorral-like equations in the present study. It is constructed based on the combination of David Eyre’s time stepping scheme and Schur complement approach. Although the presented method is general and independent to the choice of homogeneous free energy density function term, logarithmic and polynomial energy functions are specifically considered in this paper. The method is applied to study the spinodal decomposition in multi component systems and optimal space tiling problems. A penalization strategy is developed, in the case of later problem, to avoid trivial solutions. Extensive numerical experiments demonstrate the success and performance of the presented method. According to the numerical results, the method is convergent and energy stable, independent to the choice of time stepsize. Its MATLAB implementation is included in the appendix for the numerical evaluation of algorithm and reproduction of the presented results.