期刊
JOURNAL OF SCIENTIFIC COMPUTING
卷 78, 期 3, 页码 1467-1487出版社
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-018-0832-5
关键词
Thin film epitaxy; Gradient flow; Energy stable; Coarsening dynamics
资金
- Directorate for Mathematical and Physical Sciences [DMS-1620262]
We develop in this paper highly efficient, second order and unconditionally energy stable schemes for the epitaxial thin film growth models by using the scalar auxiliary variable (SAV) approach. A main difficulty here is that the nonlinear potential for the model without slope selection is not bounded from below so the SAV approach can not be directly applied. We overcome this difficulty with a suitable splitting of the total free energy density into two parts such that the integral of the part involving the nonlinear potential becomes bounded from below so that the SAV approach can be applied. We then construct a set of linear, second-order and unconditionally energy stable schemes for the reformulated systems. These schemes lead to decoupled linear equations with constant coefficients at each time step so that they can be implemented easily and very efficiently. We present ample numerical results to demonstrate the stability and accuracy of our SAV schemes.
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