Stabilized Invariant Energy Quadratization (S-IEQ) Method for the Molecular Beam Epitaxial Model Without Slope Section
Year: 2021
Author: Hui Zhang, Xiaofeng Yang, Jun Zhang
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 5 : pp. 642–655
Abstract
The design of numerical approaches for the molecular beam epitaxy models has always been a hot issue in numerical analysis, in which one of the main challenges for algorithm design is how to establish a high-order time-accurate numerical method with unconditional energy stability. The numerical method developed in this paper is based on the “stabilized-Invariant Energy Quadratization” (S-IEQ) approach. Its novelty is that by adding a very simple linear stabilization term, the difficulty that the original energy potential for the no-slope selection case is not bounded from below can be easily overcome. Then by using the standard format of the IEQ method, we can easily obtain a linear, unconditionally energy stable, and second-order time accurate scheme for solving the system. We further implement various numerical examples to demonstrate the stability and accuracy of the proposed scheme.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2021-IJNAM-19386
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 5 : pp. 642–655
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Molecular beam epitaxy linear second-order unconditional energy stability.