期刊
MATHEMATICS OF COMPUTATION
卷 87, 期 312, 页码 1859-1885出版社
AMER MATHEMATICAL SOC
DOI: 10.1090/mcom/3262
关键词
Thin film growth; exponential time differencing; Fourier collocation; linear convex splitting; energy stability; error estimates
资金
- US National Science Foundation [DMS-1521965]
- Hong Kong Research Grant Council GRF grant [15302214]
- China Postdoctoral Science Foundation [2017M610748]
- NSFC/RGC Joint Research Scheme [N_HKBU204/12, 11261160486]
- Hong Kong Polytechnic University [1-ZE33]
- NSFC [11471046, 11571045]
- Ministry of Education Program for New Century Excellent Talents Project [NCET-12-0053]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1521965] Funding Source: National Science Foundation
In this paper, we propose a class of exponential time differencing (ETD) schemes for solving the epitaxial growth model without slope selection. A linear convex splitting is first applied to the energy functional of the model, and then Fourier collocation and ETD-based multistep approximations are used respectively for spatial discretization and time integration of the corresponding gradient flow equation. Energy stabilities and error estimates of the first and second order ETD schemes are rigorously established in the fully discrete sense. We also numerically demonstrate the accuracy of the proposed schemes and simulate the coarsening dynamics with small diffusion coefficients. The results show the logarithm law for the energy decay and the power laws for growth of the surface roughness and the mound width, which are consistent with the existing theories in the literature.
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