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Volume 15, Issue 2
A Relaxed Decoupled Second-Order Energy-Stable Scheme for the Binary Phase-Field Crystal Model

Xin Zhang, Junxiang Yang & Zhijun Tan

East Asian J. Appl. Math., 15 (2025), pp. 344-372.

Published online: 2025-01

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  • Abstract

In this study, we construct a relaxed second-order time-accurate scheme for the binary phase-field crystal model based on the recent paper [J. Wu, J. Yang and Z. Tan, Eng. Comput. (2023)]. This scheme can significantly improve the consistency between original and modified energies. Using the exponential SAV method, we construct the first- and second-order time-accurate schemes by using the backward Euler formula and the second-order backward difference formula, respectively. Then a new second-order numerical scheme with relaxation is developed. This new numerical scheme satisfies the energy dissipation law. Meanwhile, it is fully decoupled and efficient. Extensive numerical experiments are carried out in 2D and 3D to verify the accuracy and stability of the proposed scheme, as well as its ability to improve the consistency between the original energy and modified energy.

  • AMS Subject Headings

65M10, 78A48

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-15-344, author = {Zhang , XinYang , Junxiang and Tan , Zhijun}, title = {A Relaxed Decoupled Second-Order Energy-Stable Scheme for the Binary Phase-Field Crystal Model}, journal = {East Asian Journal on Applied Mathematics}, year = {2025}, volume = {15}, number = {2}, pages = {344--372}, abstract = {

In this study, we construct a relaxed second-order time-accurate scheme for the binary phase-field crystal model based on the recent paper [J. Wu, J. Yang and Z. Tan, Eng. Comput. (2023)]. This scheme can significantly improve the consistency between original and modified energies. Using the exponential SAV method, we construct the first- and second-order time-accurate schemes by using the backward Euler formula and the second-order backward difference formula, respectively. Then a new second-order numerical scheme with relaxation is developed. This new numerical scheme satisfies the energy dissipation law. Meanwhile, it is fully decoupled and efficient. Extensive numerical experiments are carried out in 2D and 3D to verify the accuracy and stability of the proposed scheme, as well as its ability to improve the consistency between the original energy and modified energy.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2023-159.170324}, url = {http://global-sci.org/intro/article_detail/eajam/23753.html} }
TY - JOUR T1 - A Relaxed Decoupled Second-Order Energy-Stable Scheme for the Binary Phase-Field Crystal Model AU - Zhang , Xin AU - Yang , Junxiang AU - Tan , Zhijun JO - East Asian Journal on Applied Mathematics VL - 2 SP - 344 EP - 372 PY - 2025 DA - 2025/01 SN - 15 DO - http://doi.org/10.4208/eajam.2023-159.170324 UR - https://global-sci.org/intro/article_detail/eajam/23753.html KW - Binary phase-field crystal, unconditional energy stability, relaxed technique, second-order scheme. AB -

In this study, we construct a relaxed second-order time-accurate scheme for the binary phase-field crystal model based on the recent paper [J. Wu, J. Yang and Z. Tan, Eng. Comput. (2023)]. This scheme can significantly improve the consistency between original and modified energies. Using the exponential SAV method, we construct the first- and second-order time-accurate schemes by using the backward Euler formula and the second-order backward difference formula, respectively. Then a new second-order numerical scheme with relaxation is developed. This new numerical scheme satisfies the energy dissipation law. Meanwhile, it is fully decoupled and efficient. Extensive numerical experiments are carried out in 2D and 3D to verify the accuracy and stability of the proposed scheme, as well as its ability to improve the consistency between the original energy and modified energy.

Zhang , XinYang , Junxiang and Tan , Zhijun. (2025). A Relaxed Decoupled Second-Order Energy-Stable Scheme for the Binary Phase-Field Crystal Model. East Asian Journal on Applied Mathematics. 15 (2). 344-372. doi:10.4208/eajam.2023-159.170324
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