A linear second-order convex splitting scheme for the modified phase-field crystal equation with a strong nonlinear vacancy potential

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Abstract

The modified phase-field crystal (MPFC) equation was extended to the MPFC equation with a strong nonlinear vacancy potential (VMPFC) to include vacancies. In this paper, we develop a linear, second-order, and unconditionally energy stable scheme for solving the VMPFC equation by proposing a new linear convex splitting, using the Crank–Nicolson formula to the contractive part and the second-order Adams–Bashforth formula to the expansive part, and adding a second-order Douglas–Dupont regularization. The unconditional energy stability of the developed scheme is proved. By solving the VMPFC equation, vacancies which exist in real materials can be observed in numerical simulations.

Original languageEnglish
Article number109145
JournalApplied Mathematics Letters
Volume156
DOIs
StatePublished - Oct 2024

Keywords

  • Linear convex splitting
  • Modified phase-field crystal equation
  • Strong nonlinear vacancy potential
  • Unconditional energy stability

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