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<p>In this paper, we firstly develop an efficient relaxed generalized scalar auxiliary variable method (R-GSAV) for the modified phase field crystal (MPFC) model. By using a relaxation technique for the generalized SAV approach, the constructed R-GSAV schemes can keep all the advantages of the GSAV method while dissipating a modified energy that is closer to the original energy. To keep the positivity of the introduced auxiliary variable, we then give a positivity-preserving SAV method. All the proposed schemes are proved to be unconditionally energy stable. Several numerical examples are performed to demonstrate the accuracy and efficiency of the proposed methods.</p>

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The positivity-preserving SAV approaches with relaxation for the modified phase field crystal model

  • 期刊论文

  • 发表日期：

    2025年6月3日

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  • Qing He,
  • Yuan Li,
  • Zhengguang Liu

摘要

In this paper, we firstly develop an efficient relaxed generalized scalar auxiliary variable method (R-GSAV) for the modified phase field crystal (MPFC) model. By using a relaxation technique for the generalized SAV approach, the constructed R-GSAV schemes can keep all the advantages of the GSAV method while dissipating a modified energy that is closer to the original energy. To keep the positivity of the introduced auxiliary variable, we then give a positivity-preserving SAV method. All the proposed schemes are proved to be unconditionally energy stable. Several numerical examples are performed to demonstrate the accuracy and efficiency of the proposed methods.