Efficient linear schemes with unconditional energy stability for the phase field model of solid-state dewetting problems

Chen, Jie; He, Zhengkang; Sun, Shuyu; Guo, Shimin; Chen, Zhangxin

Efficient linear schemes with unconditional energy stability for the phase field model of solid-state dewetting problems

Files

SSDSAVHOPQ.pdf (615.18 KB)

Type

Article

Authors

Chen, Jie
He, Zhengkang
Sun, Shuyu

Guo, Shimin
Chen, Zhangxin

KAUST Department

Computational Transport Phenomena Lab
Earth Science and Engineering Program
Physical Science and Engineering (PSE) Division

KAUST Grant Number

BAS/1/1351-01-01

Online Publication Date

2020-06

Print Publication Date

2020-06

Date

2020-06

Submitted Date

2018-04-11

Abstract

In this paper, we study linearly first and second order in time, uniquely solvable and unconditionally energy stable numerical schemes to approximate the phase field model of solid-state dewetting problems based on the novel “scalar auxiliary variable” (SAV) approach, a new developed efficient and accurate method for a large class of gradient flows. The schemes are based on the first order Euler method and the second order backward differential formulas (BDF2) for time discretization, and finite element methods for space discretization. The proposed schemes are proved to be unconditionally stable and the discrete equations are uniquely solvable for all time steps. Various numerical experiments are presented to validate the stability and accuracy of the proposed schemes.

Citation

sci, J. C. (2020). Efficient Linear Schemes with Unconditional Energy Stability for the Phase Field Model of Solid-State Dewetting Problems. Journal of Computational Mathematics, 38(3), 452–468. doi:10.4208/jcm.1812-m2018-0058

Acknowledgements

The work is supported by the National Natural Science Foundation of China (No.11401467), China Postdoctoral Science Foundation (No. 2013M542334. and No. 2015T81012), and Natural Science Foundation of Shaanxi Province (No. 2015JQ1012). The work is also supported in part by funding from King Abdullah University of Science and Technology (KAUST) through the grant BAS/1/1351-01-01.