Journal of Scientific Computing

, Volume 78, Issue 3, pp 1467–1487 | Cite as

Highly Efficient and Accurate Numerical Schemes for the Epitaxial Thin Film Growth Models by Using the SAV Approach

  • Qing Cheng
  • Jie ShenEmail author
  • Xiaofeng Yang


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.


Thin film epitaxy Gradient flow Energy stable Coarsening dynamics 



This work is supported in part by NSFC Grants 91630204, 11421110001 and 51661135011, and NSF Grants DMS-1720442 and DMS-1720212.


Funding was provided by Directorate for Mathematical and Physical Sciences (Grant No. DMS-1620262).


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Authors and Affiliations

  1. 1.School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific ComputingXiamen UniversityXiamenPeople’s Republic of China
  2. 2.Department of MathematicsPurdue UniversityWest LafayetteUSA
  3. 3.Department of MathematicsUniversity of South CarolinaColumbiaUSA
  4. 4.Beijing Institute for Scientific and Engineering ComputingBeijing University of TechnologyBeijingChina

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