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Volume 11, Issue 2
A $θ-L$ Formulation-Based Finite Element Method for Solving Axisymmetric Solid-State Dewetting Problems

Weijie Huang, Wei Jiang & Quan Zhao

East Asian J. Appl. Math., 11 (2021), pp. 389-405.

Published online: 2021-02

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  • Abstract

We propose a $θ-L$ formulation-based finite element method for the sharp-interface model of solid-state dewetting with axisymmetric geometry. The model describes the film/vapor interface using the radial curve in cylindrical coordinates, and is governed by a fourth-order geometric partial differential equation with complex boundary conditions at the moving contact lines. By introducing an appropriate tangential velocity, we derive an equivalent system for the original sharp-interface model. This gives the kinetic equation for the tangential angle $θ$ and the total length $L$ of the radial curve. The new formulation can alleviate the stiffness of the original model and help to maintain mesh equidistribution during the evolution. We present an efficient finite element method for solving the resulting $θ-L$ formulation based on its weak form. Numerical examples are reported to demonstrate the accuracy and efficiency of the numerical scheme.

  • AMS Subject Headings

65M60, 74H15, 65Z99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-11-389, author = {Huang , WeijieJiang , Wei and Zhao , Quan}, title = {A $θ-L$ Formulation-Based Finite Element Method for Solving Axisymmetric Solid-State Dewetting Problems}, journal = {East Asian Journal on Applied Mathematics}, year = {2021}, volume = {11}, number = {2}, pages = {389--405}, abstract = {

We propose a $θ-L$ formulation-based finite element method for the sharp-interface model of solid-state dewetting with axisymmetric geometry. The model describes the film/vapor interface using the radial curve in cylindrical coordinates, and is governed by a fourth-order geometric partial differential equation with complex boundary conditions at the moving contact lines. By introducing an appropriate tangential velocity, we derive an equivalent system for the original sharp-interface model. This gives the kinetic equation for the tangential angle $θ$ and the total length $L$ of the radial curve. The new formulation can alleviate the stiffness of the original model and help to maintain mesh equidistribution during the evolution. We present an efficient finite element method for solving the resulting $θ-L$ formulation based on its weak form. Numerical examples are reported to demonstrate the accuracy and efficiency of the numerical scheme.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.130920.071220 }, url = {http://global-sci.org/intro/article_detail/eajam/18640.html} }
TY - JOUR T1 - A $θ-L$ Formulation-Based Finite Element Method for Solving Axisymmetric Solid-State Dewetting Problems AU - Huang , Weijie AU - Jiang , Wei AU - Zhao , Quan JO - East Asian Journal on Applied Mathematics VL - 2 SP - 389 EP - 405 PY - 2021 DA - 2021/02 SN - 11 DO - http://doi.org/10.4208/eajam.130920.071220 UR - https://global-sci.org/intro/article_detail/eajam/18640.html KW - Solid-state dewetting, surface diffusion, moving contact line, $θ-L$ formulation, finite element method. AB -

We propose a $θ-L$ formulation-based finite element method for the sharp-interface model of solid-state dewetting with axisymmetric geometry. The model describes the film/vapor interface using the radial curve in cylindrical coordinates, and is governed by a fourth-order geometric partial differential equation with complex boundary conditions at the moving contact lines. By introducing an appropriate tangential velocity, we derive an equivalent system for the original sharp-interface model. This gives the kinetic equation for the tangential angle $θ$ and the total length $L$ of the radial curve. The new formulation can alleviate the stiffness of the original model and help to maintain mesh equidistribution during the evolution. We present an efficient finite element method for solving the resulting $θ-L$ formulation based on its weak form. Numerical examples are reported to demonstrate the accuracy and efficiency of the numerical scheme.

Weijie Huang, Wei Jiang & Quan Zhao. (2021). A $θ-L$ Formulation-Based Finite Element Method for Solving Axisymmetric Solid-State Dewetting Problems. East Asian Journal on Applied Mathematics. 11 (2). 389-405. doi:10.4208/eajam.130920.071220
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