Title: High efficiently numerical simulation of the TDGL equation with reticular free energy in hydrogel,
Abstract: In this paper, we focus on the numerical simulation of phase separation about
macromolecule microsphere composite (MMC) hydrogel. The model equation is based
on Time-Dependent Ginzburg-Landau (TDGL) equation with reticular free energy.
We have put forward two $L^2$ stable schemes to simulate simplified TDGL
equation. In numerical experiments, we observe that simulating the whole
process of phase separation requires a considerably long time. We also notice
that the total free energy changes significantly in initial time and varies
slightly in the following time. Based on these properties, we introduce an
adaptive strategy based on one of stable scheme mentioned. It is found that the
introduction of the time adaptivity cannot only resolve the dynamical changes
of the solution accurately but also can significantly save CPU time for the
long time simulation.