Efficient modified techniques of invariant energy quadratization approach for gradient flows
Efficient modified techniques of invariant energy quadratization approach for gradient flows
复制标题
DOI：
10.1016/j.aml.2019.06.006
复制
发表时间：
2019-12
期刊：
影响因子：
--
通讯作者：
Zhengguang Liu;Xiaoli Li
中科院分区：
文献类型：
--
作者：
Zhengguang Liu;Xiaoli Li
本文在最近发展的稳定不变能量二次化（IEQ）方法的基础上，提出了两种新的、有效的改进方法来处理梯度流中的非线性项。我们仔细而严格地证明了一类梯度流及其半离散格式的无条件能量稳定性。这种方法的贡献之一是，我们成功地找到了合适的正保持功能的平方根，并不需要添加一个正常数，不能固定之前计算。其次，所有的非线性项可以半显式地处理，并且在每个时间步只需要求解三个解耦的常系数线性方程组。最后，通过数值模拟验证了所提方法的准确性和有效性.
Two novel and efficient modified techniques based on recently developed stabilized invariant energy quadratization (IEQ) approach to deal with nonlinear terms in gradient flows are proposed in this paper. We proved the unconditional energy stability for a class of gradient flows and their semi-discrete schemes carefully and rigorously. One of the contributions for this approach is that we succeeded in finding suitable positive preserving functions in square root and do not need to add a positive constant which cannot be fixed before computing. Secondly, all nonlinear terms can be treated semi-explicitly, and one only needs to solve three decoupled linear equations with constant coefficients at each time step. Finally, several numerical simulations are demonstrated to verify the accuracy and efficiency of our proposed schemes.