 An adaptive time-stepping method for the phase-field molecular beam epitaxial growth model on evolving surfacesShijie Huang, Xufeng Xiao and Xinlong Feng Applied Mathematics and Computation, 2023, vol. 439, issue C 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. Keywords: Molecular beam epitaxial growth model; Adaptive time-stepping; Evolving surface finite element method; Stability analysis (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:439:y:2023:i:c:s0096300322006956 DOI: 10.1016/j.amc.2022.127622 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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