论文标题
梯度流的一般无条件的无条件能量稳定方案
A general class of linear unconditionally energy stable schemes for the gradient flows
论文作者
论文摘要
本文研究了一类无条件的线性能量稳定方案，用于梯度流。此类方案建立在SAV技术和一般线性时间离散化（GLTD）以及基于非线性术语的外推的线性化，并且可能是任意高阶准确且非常通用的，其中包含许多现有的SAV方案和新的SAV计划。结果表明，当GLTD在代数上稳定时，半差异的时间方案是无条件的能量稳定，并且在$ \ min \ hat {\ hat {q}，ν\} $下的订单下，在对角度的稳定性下，$ \ hat $ \ hat us $ \ hat $ \ s $} $} $} $} $} $ {表示推断点的时间数。能量稳定性结果可以很容易地扩展到完全离散的方案，例如，如果指定周期性边界条件时，则在空间中采用傅立叶光谱法。对Allen-Cahn，Cahn-Hilliard和相位场晶体模型进行了一些数值实验，以验证这些理论以及我们方案的有效性，能量稳定性和准确性。
This paper studies a class of linear unconditionally energy stable schemes for the gradient flows. Such schemes are built on the SAV technique and the general linear time discretization (GLTD) as well as the linearization based on the extrapolation for the nonlinear term, and may be arbitrarily high-order accurate and very general, containing many existing SAV schemes and new SAV schemes. It is shown that the semi-discrete-in-time schemes are unconditionally energy stable when the GLTD is algebraically stable, and are convergent with the order of $\min\{\hat{q},ν\}$ under the diagonal stability and some suitable regularity and accurate starting values, where $\hat{q}$ is the generalized stage order of the GLTD and $ν$ denotes the number of the extrapolation points in time. The energy stability results can be easily extended to the fully discrete schemes, for example, if the Fourier spectral method is employed in space when the periodic boundary conditions are specified. Some numerical experiments on the Allen-Cahn, Cahn-Hilliard, and phase field crystal models are conducted to validate those theories as well as the effectiveness, the energy stability and the accuracy of our schemes.
