Efficient numerical schemes with unconditional energy stabilities for the modified phase field crystal equation
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Liquan Mei | Xiaofeng Yang | Qi Li | Yibao Li
[1] N. Provatas,et al. Phase-field crystals with elastic interactions. , 2006, Physical review letters.
[2] Xiaoming He,et al. Linear, second order and unconditionally energy stable schemes for the viscous Cahn-Hilliard equation with hyperbolic relaxation using the invariant energy quadratization method , 2017, J. Comput. Appl. Math..
[3] Ilya Starodumov,et al. Three dimensional structures predicted by the modified phase field crystal equation , 2016 .
[4] Xiaofeng Yang,et al. Regularized linear schemes for the molecular beam epitaxy model with slope selection , 2018 .
[5] Xiaofeng Yang,et al. Second Order, Linear, and Unconditionally Energy Stable Schemes for a Hydrodynamic Model of Smectic-A Liquid Crystals , 2017, SIAM J. Sci. Comput..
[6] Jia Zhao,et al. Linear second order in time energy stable schemes for hydrodynamic models of binary mixtures based on a spatially pseudospectral approximation , 2018, Adv. Comput. Math..
[7] Xiaogang Yang,et al. Fully Discrete Second-Order Linear Schemes for Hydrodynamic Phase Field Models of Binary Viscous Fluid Flows with Variable Densities , 2018, SIAM J. Sci. Comput..
[8] M. Grant,et al. Phase-field crystal modeling and classical density functional theory of freezing , 2007 .
[9] Steven M. Wise,et al. Convergence Analysis of a Second Order Convex Splitting Scheme for the Modified Phase Field Crystal Equation , 2012, SIAM J. Numer. Anal..
[10] Jie Shen,et al. Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model , 2017, J. Comput. Phys..
[11] Lili Ju,et al. Unconditionally Energy Stable Linear Schemes for the Diffuse Interface Model with Peng–Robinson Equation of State , 2018, J. Sci. Comput..
[12] Jaemin Shin,et al. First- and second-order energy stable methods for the modified phase field crystal equation , 2017 .
[13] Xiaofeng Yang,et al. Numerical approximations for a three-component Cahn–Hilliard phase-field model based on the invariant energy quadratization method , 2017 .
[14] Lili Ju,et al. Efficient linear schemes with unconditional energy stability for the phase field elastic bending energy model , 2017 .
[15] M. Grant,et al. Modeling elastic and plastic deformations in nonequilibrium processing using phase field crystals. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.
[16] Xiaofeng Yang,et al. Numerical approximations of Allen-Cahn and Cahn-Hilliard equations , 2010 .
[17] Jie Shen,et al. A Phase-Field Model and Its Numerical Approximation for Two-Phase Incompressible Flows with Different Densities and Viscosities , 2010, SIAM J. Sci. Comput..
[18] Steven M. Wise,et al. An Energy Stable and Convergent Finite-Difference Scheme for the Modified Phase Field Crystal Equation , 2011, SIAM J. Numer. Anal..
[19] Martin Grant,et al. Modeling elasticity in crystal growth. , 2001, Physical review letters.
[20] Xiaofeng Yang,et al. Error analysis of stabilized semi-implicit method of Allen-Cahnequation , 2009 .
[21] Jia Zhao,et al. Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method , 2017, J. Comput. Phys..
[22] J. Swift,et al. Hydrodynamic fluctuations at the convective instability , 1977 .
[23] Jia Zhao,et al. Second Order Fully Discrete Energy Stable Methods on Staggered Grids for Hydrodynamic Phase Field Models of Binary Viscous Fluids , 2018, SIAM J. Sci. Comput..
[24] Xiaofeng Yang,et al. A novel linear second order unconditionally energy stable scheme for a hydrodynamic Q-tensor model of liquid crystals , 2017 .
[25] M. Dehghan,et al. The numerical simulation of the phase field crystal (PFC) and modified phase field crystal (MPFC) models via global and local meshless methods , 2016 .
[26] Yan Xu,et al. A High Order Adaptive Time-Stepping Strategy and Local Discontinuous Galerkin Method for the Modified Phase Field Crystal Equation , 2018 .
[27] M. Grasselli,et al. Energy stable and convergent finite element schemes for the modified phase field crystal equation , 2016 .
[28] Xiaofeng Yang,et al. Numerical approximations for a phase field dendritic crystal growth model based on the invariant energy quadratization approach , 2017 .
[29] Xiaofeng Yang,et al. Numerical Approximations for the Cahn–Hilliard Phase Field Model of the Binary Fluid-Surfactant System , 2017, Journal of Scientific Computing.
[30] Unconditionally stable method and numerical solution of the hyperbolic phase-field crystal equation. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.
[31] Badrinarayan P. Athreya,et al. Using the phase-field crystal method in the multi-scale modeling of microstructure evolution , 2007 .
[32] Xiaofeng Yang,et al. Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends , 2016, J. Comput. Phys..
[33] Cheng Wang,et al. Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation , 2012, J. Comput. Phys..
[34] Nikolas Provatas,et al. Phase field crystal study of deformation and plasticity in nanocrystalline materials. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.