Efficient linear schemes with unconditional energy stability for the phase field model of solid-state dewetting problems
KAUST DepartmentComputational Transport Phenomena Lab
Earth Science and Engineering Program
Physical Science and Engineering (PSE) Division
KAUST Grant NumberBAS/1/1351-01-01
Online Publication Date2020-06
Print Publication Date2020-06
Permanent link to this recordhttp://hdl.handle.net/10754/664447
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AbstractIn 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.
Citationsci, 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
SponsorsThe 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.
PublisherGlobal Science Press