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A structure-preserving and variable-step BDF2 Fourier pseudo-spectral method for the two-mode phase field crystal model

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  • Li, Dongfang
  • Li, Xiaoxi
  • Mei, Ming
  • Yuan, Wanqiu

Abstract

For the two-mode phase field crystal models, the evolutions of the solutions and energy vary fast at certain time. To resolve varying time scales efficiently and reduce the computational cost, a variable-step BDF2 Fourier pseudo-spectral method is proposed. It is shown that the fully-discrete scheme is volume-conserving and unconditional energy-stable. Moreover, a robust error estimate is established by using the discrete orthogonal convolution kernels and the corresponding convolution inequalities. Numerical experiments by using the random and adaptive time-stepping strategies are presented to confirm the effectiveness of the scheme.

Suggested Citation

  • Li, Dongfang & Li, Xiaoxi & Mei, Ming & Yuan, Wanqiu, 2023. "A structure-preserving and variable-step BDF2 Fourier pseudo-spectral method for the two-mode phase field crystal model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 483-506.
    • Handle: RePEc:eee:matcom:v:205:y:2023:i:c:p:483-506
    DOI: 10.1016/j.matcom.2022.10.009
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    Keywords

    Variable-step BDF2 scheme; Two-mode phase-field crystal model; Robust L2 error estimate; Structure-preserving;
    All these keywords.

    JEL classification:

    • L2 - Industrial Organization - - Firm Objectives, Organization, and Behavior

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