Numerical analysis of a continuum model of phase transition
SIAM Journal on Numerical Analysis
Journal of Scientific Computing
Moving mesh methods with locally varying time steps
Journal of Computational Physics
On large time-stepping methods for the Cahn--Hilliard equation
Applied Numerical Mathematics
An efficient algorithm for solving the phase field crystal model
Journal of Computational Physics
Journal of Computational Physics
An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation
SIAM Journal on Numerical Analysis
Journal of Scientific Computing
SIAM Journal on Numerical Analysis
An Adaptive Time-Stepping Strategy for the Molecular Beam Epitaxy Models
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Hi-index | 31.45 |
In this work, we will propose an adaptive time step method for simulating the dynamics of the phase field crystal (PFC) model. The numerical simulation of the PFC model needs long time to reach steady state, and then large time-stepping method is necessary. Unconditionally energy stable schemes are used to solve the PFC model. The time steps are adaptively determined based on the time derivative of the corresponding energy. It is found that the use of the proposed time step adaptivity cannot only resolve the steady state solution, but also the dynamical development of the solution efficiently and accurately. The numerical experiments demonstrate that the CPU time is significantly saved for long time simulations.