scholarly journals Efficient linear and unconditionally energy stable schemes for the modified phase field crystal equation

2021 ◽  
Author(s):  
Xiaoli Li ◽  
Jie Shen
Keyword(s):  
Phase Field ◽  
Energy Stable Schemes ◽  
Energy Stable ◽  
Phase Field Crystal

Efficient numerical algorithms for the phase field crystal equation

2021 ◽  
pp. 2150042
Author(s):  
Qingqu Zhuang ◽  
Shuying Zhai ◽  
Zhifeng Weng
Keyword(s):  
Free Energy ◽  
Lower Bound ◽  
Numerical Simulations ◽  
Lagrange Multiplier ◽  
Phase Field ◽  
Numerical Algorithms ◽  
Energy Potential ◽  
Energy Stable ◽  
2D And 3D ◽  
Phase Field Crystal

In this paper, based on the Lagrange Multiplier approach in time and the Fourier-spectral scheme for space, we propose efficient numerical algorithms to solve the phase field crystal equation. The numerical schemes are unconditionally energy stable based on the original energy and do not need the lower bound hypothesis of the nonlinear free energy potential. The unconditional energy stability of the three semi-discrete schemes is proven. Several numerical simulations in 2D and 3D are demonstrated to verify the accuracy and efficiency of our proposed schemes.

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