Efficient modified stabilized invariant energy quadratization approaches for phase-field crystal equation
Efficient modified stabilized invariant energy quadratization approaches for phase-field crystal equation
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DOI：
10.1007/s11075-019-00804-9
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发表时间：
2019-09
影响因子：
2.1
通讯作者：
Zhengguang Liu;Xiaoli Li
中科院分区：
文献类型：
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作者：
Zhengguang Liu;Xiaoli Li
相场晶体方程是六阶非线性抛物线方程，可用于模拟外延生长、材料硬度和相变等各种现象。我们为相场晶体模型提出了一系列具有无条件能量稳定性的有效修正稳定不变能量二次化方法。首先，我们提出了一个更合适的严格平方根的正保留函数，并考虑改进的不变能量二次化（MIEQ）方法。其次，考虑了一系列有效且合适的平方根泛函H(phi)，并开发了改进的稳定不变能量二次化（MSIEQ）方法。我们仔细而严格地证明了半离散方案的无条件能量稳定性和最优误差估计。经典 IEQ、MIEQ 和 MSIEQ 方法的比较研究被认为显示了准确性和效率。最后，我们提出了各种二维数值模拟来证明稳定性和准确性。
The phase-field crystal equation is a sixth-order nonlinear parabolic equation and can be applied to simulate various phenomena such as epitaxial growth, material hardness, and phase transition. We propose a series of efficient modified stabilized invariant energy quadratization approaches with unconditional energy stability for the phase-field crystal model. Firstly, we propose a more suitable positive preserving function strictly in square root and consider a modified invariant energy quadratization (MIEQ) approach. Secondly, a series of efficient and suitable functionalsH(ϕ) in square root are considered and the modified stabilized invariant energy quadratization (MSIEQ) approaches are developed. We prove the unconditional energy stability and optimal error estimates for the semi-discrete schemes carefully and rigorously. A comparative study of classical IEQ, MIEQ, and MSIEQ approaches is considered to show the accuracy and efficiency. Finally, we present various 2D numerical simulations to demonstrate the stability and accuracy.