| 相场晶体方程的一个高精度能量稳定数值格式 |
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| 引用本文： | 李贵川,赖倩,胡劲松.相场晶体方程的一个高精度能量稳定数值格式[J].四川大学学报(自然科学版),2022,59(3):031004-36. |
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| 作者姓名： | 李贵川 赖倩 胡劲松 |
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| 作者单位： | 西华大学土木建筑与环境学院,西华大学理学院,西华大学理学院 |
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| 基金项目： | 四川省应用基础研究项目(2019YJ0387) |
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| 摘 要： | 针对具有周期边界条件的相场晶体方程，本文提出了一个具有能量稳定性的高精度数值格式.该格式基于方程的能量泛函结构，在空间上采用Fourier拟谱逼近，在时间上进行三阶精度的向后差分离散，并在格式中增加Douglas-Dupont正则项，以保证格式的能量稳定性.本文证明了数值解的存在唯一性及数值格式的能量稳定性.数值算例验证了算法的高精度和稳定性.
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| 关 键 词： | 相场晶体方程 能量稳定性 Fourier拟谱逼近 后向微分形式 |
| 收稿时间： | 2021/11/9 0:00:00 |
| 修稿时间： | 2022/1/7 0:00:00 |
An high-accuracy energy stable numerical scheme for the phase field crystal equation |
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| LI Gui-Chuan,LAI Qian and HU Jin-Song.An high-accuracy energy stable numerical scheme for the phase field crystal equation[J].Journal of Sichuan University (Natural Science Edition),2022,59(3):031004-36. |
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| Authors: | LI Gui-Chuan LAI Qian and HU Jin-Song |
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| Institution: | School of Architecture and Civil Engineering, Xihua University,School of Science, Xihua University,School of Science, Xihua University |
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| Abstract: | In this paper, we propose an energy stable numerical scheme for the phase field crystal equation with periodic boundary condition. This scheme is based on the structure of the energy functional. A Fourier pesudo spectral approximation is applied in space as well as a third order backward differentiation scheme is applied in the temporal approximation for the equation. Meanwhile, a Douglas-Dupont type regularization term is added to ensure the modified energy stability. The unique solvability and energy stability of the scheme are established. Finally, some numerical examples are presented to confirm the robustness and accuracy of the scheme. |
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| Keywords: | Phase field crystal equation Energy stability Fourier pseudo spectal approximation Backward differentiation formula |
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