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Highly efficient and fully decoupled BDF time-marching schemes with unconditional energy stabilities for the binary phase-field crystal models

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Abstract

In this paper, we present totally decoupled, efficiently linear, and energy stable schemes for solving the binary phase-field crystal model. We introduce a new auxiliary variable to reformulate the model. Based on the backward Euler formula and the second-order backward difference formula (BDF2), we construct the first- and second-order time-accurate schemes, respectively. The modified energy not only can be calculated directly from the schemes but also satisfies the energy dissipation law. In each time step, we solve two linear elliptic equations with constant coefficients and other variables are explicitly computed. The fast Fourier transform (FFT) is adopted to accelerate the convergence. Thus, the computation is highly efficient. Various benchmark numerical experiments in 2D and 3D, such as the binary crystal growth, phase separation with vacancies, are performed to show the efficiency and performance of the proposed schemes.

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Acknowledgements

The work of Z. Tan is supported by the National Nature Science Foundation of China (11971502), Guangdong Natural Science Foundation (2022A1515010426)，Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University (2020B1212060032), and Key-Area Research and Development Program of Guangdong Province (2021B0101190003). J. Yang is supported by the China Postdoctoral Science Foundation (No. 2022M713639).

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  1. School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou, 510275, China

    Jingwen Wu, Junxiang Yang & Zhijun Tan

  2. Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou, 510275, China

    Zhijun Tan

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Wu, J., Yang, J. & Tan, Z. Highly efficient and fully decoupled BDF time-marching schemes with unconditional energy stabilities for the binary phase-field crystal models. Engineering with Computers 39, 3157–3181 (2023). https://doi.org/10.1007/s00366-022-01727-1

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