High-order energy stable schemes of incommensurate phase-field crystal model

Electronic Research Archive ◽

10.3934/era.2020059 ◽

2020 ◽

Vol 28 (2) ◽

pp. 1077-1093

Author(s):

Kai Jiang ◽

◽

Wei Si

Keyword(s):

Phase Field ◽

Incommensurate Phase ◽

Order Energy ◽

Crystal Model ◽

Energy Stable Schemes ◽

Energy Stable ◽

Phase Field Crystal

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Linear second order energy stable schemes for phase field crystal growth models with nonlocal constraints

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2019.07.030 ◽

2020 ◽

Vol 79 (3) ◽

pp. 764-788 ◽

Author(s):

Xiaobo Jing ◽

Qi Wang

Keyword(s):

Crystal Growth ◽

Phase Field ◽

Growth Models ◽

Second Order ◽

Order Energy ◽

Energy Stable Schemes ◽

Energy Stable ◽

Nonlocal Constraints ◽

Phase Field Crystal

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Long-time simulation of the phase-field crystal equation using high-order energy-stable CSRK methods

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2020.112981 ◽

2020 ◽

Vol 364 ◽

pp. 112981 ◽

Author(s):

Jaemin Shin ◽

Hyun Geun Lee ◽

June-Yub Lee

Keyword(s):

Phase Field ◽

Order Energy ◽

Time Simulation ◽

Long Time ◽

Energy Stable ◽

Phase Field Crystal

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A linearly second-order energy stable scheme for the phase field crystal model

Applied Numerical Mathematics ◽

10.1016/j.apnum.2019.01.017 ◽

2019 ◽

Vol 140 ◽

pp. 134-164 ◽

Author(s):

Shuaichao Pei ◽

Yanren Hou ◽

Bo You

Keyword(s):

Phase Field ◽

Second Order ◽

Order Energy ◽

Crystal Model ◽

Energy Stable ◽

Energy Stable Scheme ◽

Stable Scheme ◽

Phase Field Crystal

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Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model

Journal of Computational Physics ◽

10.1016/j.jcp.2016.10.020 ◽

2017 ◽

Vol 330 ◽

pp. 1116-1134 ◽

Author(s):

Xiaofeng Yang ◽

Daozhi Han

Keyword(s):

Phase Field ◽

Second Order ◽

Crystal Model ◽

Energy Stable Schemes ◽

Energy Stable ◽

Phase Field Crystal

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First- and second-order energy stable methods for the modified phase field crystal equation

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2017.03.033 ◽

2017 ◽

Vol 321 ◽

pp. 1-17 ◽

Author(s):

Hyun Geun Lee ◽

Jaemin Shin ◽

June-Yub Lee

Keyword(s):

Phase Field ◽

Second Order ◽

Order Energy ◽

Energy Stable ◽

Phase Field Crystal

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

Science China Mathematics ◽

10.1007/s11425-020-1867-8 ◽

2021 ◽

Author(s):

Xiaoli Li ◽

Jie Shen

Keyword(s):

Phase Field ◽

Energy Stable Schemes ◽

Energy Stable ◽

Phase Field Crystal

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Fast, unconditionally energy stable large time stepping method for a new Allen–Cahn type square phase-field crystal model

Applied Mathematics Letters ◽

10.1016/j.aml.2019.06.007 ◽

2019 ◽

Vol 98 ◽

pp. 248-255 ◽

Author(s):

Fubiao Lin ◽

Xiaoming He ◽

Xiaoxia Wen

Keyword(s):

Phase Field ◽

Time Stepping ◽

Crystal Model ◽

Energy Stable ◽

Phase Field Crystal

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A second-order, uniquely solvable, energy stable BDF numerical scheme for the phase field crystal model

Applied Numerical Mathematics ◽

10.1016/j.apnum.2018.07.003 ◽

2018 ◽

Vol 134 ◽

pp. 46-65 ◽

Author(s):

Qi Li ◽

Liquan Mei ◽

Bo You

Keyword(s):

Phase Field ◽

Numerical Scheme ◽

Second Order ◽

Crystal Model ◽

Energy Stable ◽

Phase Field Crystal

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Enabling simulations of grains within a full rotation range in amplitude expansion of the phase-field crystal model

Physical Review E ◽

10.1103/physreve.101.043309 ◽

2020 ◽

Vol 101 (4) ◽

Author(s):

Matjaž Berčič ◽

Goran Kugler

Keyword(s):

Phase Field ◽

Crystal Model ◽

Full Rotation ◽

Phase Field Crystal

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Fourier-spectral-method implementation of deformation in the phase-field crystal model: Further development

10.1063/5.0022984 ◽

2020 ◽

Author(s):

Nirand Pisutha-Arnond

Keyword(s):

Spectral Method ◽

Phase Field ◽

Fourier Spectral Method ◽

Crystal Model ◽

Further Development ◽

Phase Field Crystal

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