### A θ-L APPROACH FOR SOLVING SOLID-STATE DEWETTING PROBLEMS

Weijie Huang1, Wei Jiang2,3, Yan Wang4

1. 1. Beijing Computational Science Research Center, Beijing 100193, China;
2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;
3. Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan 430072, China;
4. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China
• Received:2020-02-19 Revised:2020-09-01 Online:2022-03-15 Published:2022-03-29
• Contact: Yan Wang,Email: wang.yan@mail.ccnu.edu.cn
• Supported by:
This work was partially supported by the National Natural Science Foundation of China under Grant Nos.11871384(W.J.),12001034(W.H.),12001221(Y.W.),and 91630207(W.H.),by the Fundamental Research Funds for the Central Universities under Grant CCNU19TD010(Y.W.) and by the Natural Science Foundation of Hubei Province under Grant Nos.2018CFB466(W.J.) and 2020CFB221(Y.W.).

Weijie Huang, Wei Jiang, Yan Wang. A θ-L APPROACH FOR SOLVING SOLID-STATE DEWETTING PROBLEMS[J]. Journal of Computational Mathematics, 2022, 40(2): 275-293.

We propose a θ-L approach for solving a sharp-interface model about simulating solidstate dewetting of thin films with isotropic/weakly anisotropic surface energies. The sharpinterface model is governed by surface diffusion and contact line migration. For solving the model, traditional numerical methods usually suffer from the severe stability constraint and/or the mesh distribution trouble. In the θ-L approach, we introduce a useful tangential velocity along the evolving interface and utilize a new set of variables (i.e., the tangential angle θ and the total length L of the interface curve), so that it not only could reduce the stiffness resulted from the surface tension, but also could ensure the mesh equidistribution property during the evolution. Furthermore, it can achieve second-order accuracy when implemented by a semi-implicit linear finite element method. Numerical results are reported to demonstrate that the proposed θ-L approach is efficient and accurate.

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