In this paper,based on the Lagrange Multiplier approach in time and the Fourierspectral scheme for space,we propose efficient numerical algorithms to solve the phase field crystal equation.The numerical schemes are u...In this paper,based on the Lagrange Multiplier approach in time and the Fourierspectral 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.展开更多
基金The work of Q.Zhuang is supported by the National Natural Science Foundation of China(No.11771083)The research of S.Zhai is supported in part by the Natural Science Foundation of China(No.11701196)+3 种基金the Natural Science Foundation of Fujian Province(No.2020J01074)The work of Z.Weng is supported in part by the Natural Science Foundation of China(No.11701197)Supported by the Fundamental Research Funds for the Central Universities(No.ZQN-702)the Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education(Xiangtan University)(No.2020ICIP03).
文摘In this paper,based on the Lagrange Multiplier approach in time and the Fourierspectral 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.
