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Volume 40, Issue 2
A $\theta$-$L$ Approach for Solving Solid-State Dewetting Problems

Weijie Huang, Wei Jiang & Yan Wang

DOI: 10.4208/jcm.2010-m2020-0040

J. Comp. Math., 40 (2022), pp. 275-293.

Published online: 2022-01

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  • Abstract

We propose a $\theta$-$L$ approach for solving a sharp-interface model about simulating solid-state dewetting of thin films with isotropic/weakly anisotropic surface energies. The sharp-interface 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 $\theta$-$L$ approach, we introduce a useful tangential velocity along the evolving interface and utilize a new set of variables (i.e., the tangential angle $\theta$ 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 $\theta$-$L$ approach is efficient and accurate.

  • Keywords

Solid-state dewetting, Surface diffusion, Moving contact lines, Anisotropic surface energy, $\theta$-$L$ formulation, Finite element method.

  • AMS Subject Headings

65M06, 65M12, 65M60, 75G15, 74H15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

huangwj@csrc.ac.cn (Weijie Huang)

jiangwei1007@whu.edu.cn (Wei Jiang)

wang.yan@mail.ccnu.edu.cn (Yan Wang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-40-275, author = {Huang , WeijieJiang , Wei and Wang , Yan}, title = {A $\theta$-$L$ Approach for Solving Solid-State Dewetting Problems}, journal = {Journal of Computational Mathematics}, year = {2022}, volume = {40}, number = {2}, pages = {275--293}, abstract = {

We propose a $\theta$-$L$ approach for solving a sharp-interface model about simulating solid-state dewetting of thin films with isotropic/weakly anisotropic surface energies. The sharp-interface 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 $\theta$-$L$ approach, we introduce a useful tangential velocity along the evolving interface and utilize a new set of variables (i.e., the tangential angle $\theta$ 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 $\theta$-$L$ approach is efficient and accurate.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2010-m2020-0040}, url = {http://global-sci.org/intro/article_detail/jcm/20187.html} }
TY - JOUR T1 - A $\theta$-$L$ Approach for Solving Solid-State Dewetting Problems AU - Huang , Weijie AU - Jiang , Wei AU - Wang , Yan JO - Journal of Computational Mathematics VL - 2 SP - 275 EP - 293 PY - 2022 DA - 2022/01 SN - 40 DO - http://doi.org/10.4208/jcm.2010-m2020-0040 UR - https://global-sci.org/intro/article_detail/jcm/20187.html KW - Solid-state dewetting, Surface diffusion, Moving contact lines, Anisotropic surface energy, $\theta$-$L$ formulation, Finite element method. AB -

We propose a $\theta$-$L$ approach for solving a sharp-interface model about simulating solid-state dewetting of thin films with isotropic/weakly anisotropic surface energies. The sharp-interface 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 $\theta$-$L$ approach, we introduce a useful tangential velocity along the evolving interface and utilize a new set of variables (i.e., the tangential angle $\theta$ 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 $\theta$-$L$ approach is efficient and accurate.

Huang , WeijieJiang , Wei and Wang , Yan. (2022). A $\theta$-$L$ Approach for Solving Solid-State Dewetting Problems. Journal of Computational Mathematics. 40 (2). 275-293. doi:10.4208/jcm.2010-m2020-0040
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