相场方程的高效数值算法

In this article, we overview recent developments of numerical methods for phase-field equations. The main difficulty for numerically solving phase-field equations is about a severe restriction on the time step due to nonlinearity and high order differential terms, while it usually requires a very long time simulation to reach the steady state. It is known that phase-field models satisfy a nonlinear stability relationship, called energy stability, which means that the free energy functional decays in time. It has attracted more and more attention to design numerical schemes inheriting the energy stability so that the numerical simulation may use large time steps and keep the accuracy. For some popularly studied phase-field equations, this article will present several widely used highly efficient numerical schemes and show an adaptive time-stepping strategy based on the changing rate in time of the energy functional, which could guarantee the accuracy and stability of the numerical solution and improves the computational efficiency significantly.