A linear, high-order, and unconditionally energy stable scheme for the epitaxial thin film growth model without slope selection

Jaemin Shin, Hyun Geun Lee

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

The epitaxial thin film growth model without slope selection is the L2-gradient flow of energy with a logarithmic potential in terms of the gradient of a height function. A challenge to numerically solving the model is how to treat the nonlinear term to preserve energy stability without compromising accuracy and efficiency. To resolve this problem, we present a high-order energy stable scheme by placing the linear and nonlinear terms in the convex and concave parts, respectively, and employing the specially designed implicit–explicit Runge–Kutta method. As a result, our scheme is linear, high-order accurate in time, and unconditionally energy stable. We show analytically that the scheme is unconditionally uniquely solvable and energy stable. Numerical experiments are presented to demonstrate the accuracy, efficiency, and energy stability of the proposed scheme.

Original languageEnglish
Pages (from-to)30-42
Number of pages13
JournalApplied Numerical Mathematics
Volume163
DOIs
StatePublished - May 2021

Keywords

  • Epitaxial thin film growth
  • High-order time accuracy
  • Implicit–explicit Runge–Kutta
  • Linear convex splitting
  • Unconditional energy stability
  • Unconditional unique solvability

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