Matlab code of paper "Efficient second-order unconditionally stable numerical schemes for the modified phase field crystal model with long-range interaction, 389, 113335, 2021." by Qi Li, Liquan Mei, and Yibao Li.
If you use the code, please cite:
Qi Li, Liquan Mei, and Yibao Li. Efficient second-order unconditionally stable numerical schemes for the modified phase field crystal model with long-range interaction. Journal of Computational and Applied Mathematics, 389, 113335, 2021.
or
@article{LI2021113335,
title = "Efficient second-order unconditionally stable numerical schemes for the modified phase field crystal model with long-range interaction",
journal = "Journal of Computational and Applied Mathematics",
author = "Qi Li and Liquan Mei and Yibao Li",
volume = "389",
pages = "113335",
year = "2021",
issn = "0377-0427",
doi = "https://doi.org/10.1016/j.cam.2020.113335",
url = "http://www.sciencedirect.com/science/article/pii/S0377042720306269"
}
You can follow the steps below to run this program:
- Temporal accuracy test
cd example06_2D_CN_in_Time_exact_o_2
run main06 % need long time
cd ../example06_2D_CN_in_Time_exact_ok
run main06 % need long time
cd ../example09_2D_BDF_in_Time_exact_o_2
run main09 % need long time
cd ../example09_2D_BDF_in_Time_exact_ok
run main09 % need long time
cd ../
run error_plotGet three figures in folder figure_MPFC_SAV. This step will take a long time.
- Comparison with IEQ approach
cd example06_2D_CN_in_time_exact_SAVvsIEQ
run main06_SAV
run main06_IEQ
cd ../example09_2D_CN_in_time_exact_SAVvsIEQ
run main09_SAV
run main09_IEQGet the numerical results displayed in Table 1.
- Energy stability test
cd ../example14_2D_CN_energy_and_mass_ok
run main14_1_1
run main14_1_2
run main14_2_1
run main14_2_2
run main14_2_3
run main14_fig3
cd ../example15_2D_BDF_energy_and_mass_ok
run main15_fig3- The evolution of the phase transition behavior in 2D
cd ../example16_2D_random_init_v2
run main16_2_1
run main16_2_2
run main16_2_3
run main16_plotNote: need to change the variable dirname.
- The evolution of the phase transition behavior in 3D
cd ../example19_3D_random_init_ok_L50
run main19_2_1
run main19_2_2
run main19_2_3
% Plot
run main19_2_plot
run main19_2_plot_slice
run main19_2_plot_slice3Note: need to change the variable dirname.
- Crystal growth in 2D
cd ../example17_2D_3Difference_Crystral_growth_ok
run main17_2
run main17_plot
cd ../example21_2D_single_init
run main21_1
run main21_plot- Crystal growth in 3D
cd ../example18_3D_random_init_ok
run main18_2
run main18_2_plot_sliceAfter done the above steps, some figures will be generated in folder figure_MPFC_SAV, and then using the application JPG2EPS.exe to convert these figures into EPS format.
If you have any questions, please contact liqihao@chd.edu.cn.