论文标题
相位场晶体模型的自适应BDF2隐式时间步变方法
An adaptive BDF2 implicit time-stepping method for the phase field crystal model
论文作者
论文摘要
为相场晶体模型分析了一种自适应BDF2隐式时间步变方法。如果时间键比$ r_k：=τ_k/τ_{k-1} <3.561 $，建议的方法被证明是在离散级别保留修改的能量耗散定律，这是对常见差异问题的可变step bdf2方案的最新零稳定性限制。通过使用离散的正交卷积内核和相应的卷积不平等，在弱的步长限制下建立了最佳的$ l^2 $规范误差估计$ 0 <r_k <3.561 $确保能量稳定性。这是从理论上证明这种错误估计的第一次，对于非线性抛物线方程。根据对随机时间网格的充分测试，建议采用有用的自适应时间稳定策略来有效捕获多尺度行为并加速数值模拟。
An adaptive BDF2 implicit time-stepping method is analyzed for the phase field crystal model. The suggested method is proved to preserve a modified energy dissipation law at the discrete levels if the time-step ratios $r_k:=τ_k/τ_{k-1}<3.561$, a recent zero-stability restriction of variable-step BDF2 scheme for ordinary differential problems. By using the discrete orthogonal convolution kernels and the corresponding convolution inequalities, an optimal $L^2$ norm error estimate is established under the weak step-ratio restriction $0<r_k<3.561$ ensuring the energy stability. This is the first time such error estimate is theoretically proved for a nonlinear parabolic equation. On the basis of ample tests on random time meshes, a useful adaptive time-stepping strategy is suggested to efficiently capture the multi-scale behaviors and to accelerate the numerical simulations.
