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Abstract:
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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Source :
JOURNAL OF SCIENTIFIC COMPUTING
ISSN: 0885-7474
Year: 2019
Issue: 3
Volume: 78
Page: 1467-1487
2 . 5 0 0
JCR@2022
ESI Discipline: MATHEMATICS;
ESI HC Threshold:54
JCR Journal Grade:1
Cited Count:
WoS CC Cited Count: 68
SCOPUS Cited Count: 70
ESI Highly Cited Papers on the List: 26 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 8
Affiliated Colleges: