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An adaptive time-stepping method for the phase-field molecular beam epitaxial growth model on evolving surfaces

Author

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  • Huang, Shijie
  • Xiao, Xufeng
  • Feng, Xinlong

Abstract

In this paper, a stable and efficient numerical method is presented to simulate the phase-field molecular beam epitaxial growth model on evolving surfaces. The energy dissipation law of the phase-field molecular beam epitaxial growth model on evolving surfaces does not hold for the arbitrary surface velocity which can be considered as a result of external force of the system. However, the stiffness caused by the model’s small interfacial parameter makes conventional numerical approach unstable. Hence, a stabilized semi-implicit method combined with the evolving surface finite element method is proposed and analyzed for the space-time discretization. Moreover, to improve the computational efficiency, an adaptive time-stepping technique which takes account of the energy evolution and surface velocity is also provided. Numerical examples are given to verify the effectiveness of the proposed strategy. Several numerical simulations are performed to explore the beam epitaxial growth on evolving surfaces.

Suggested Citation

  • Huang, Shijie & Xiao, Xufeng & Feng, Xinlong, 2023. "An adaptive time-stepping method for the phase-field molecular beam epitaxial growth model on evolving surfaces," Applied Mathematics and Computation, Elsevier, vol. 439(C).
    • Handle: RePEc:eee:apmaco:v:439:y:2023:i:c:s0096300322006956
    DOI: 10.1016/j.amc.2022.127622
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    Cited by:

    1. Yang, Junxiang & Lee, Dongsun & Kwak, Soobin & Ham, Seokjun & Kim, Junseok, 2024. "The Allen–Cahn model with a time-dependent parameter for motion by mean curvature up to the singularity," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

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