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Volume 12, Issue 4
Convex Splitting Method for Strongly Anisotropic Solid-State Dewetting Problems in Two Dimensions

Miaoyu Dai, Zhongyi Huang & Wei Zhu

East Asian J. Appl. Math., 12 (2022), pp. 791-820.

Published online: 2022-08

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  • Abstract

A novel sharp-interface model for the solid-state dewetting problem in the two-dimensional case is proposed. Instead of incorporating the Willmore energy or an $L_2$-curvature regularization term as is done in previous studies, we add an $L_1$-curvature regularization to the interfacial energy functional in order to make this problem well-posed. Experiments show that such regularization improves the computational efficiency. In strongly anisotropic case, we consider a new numerical scheme based on the convex-splitting idea. This approach remarkably relax the restriction on the time step. In addition, we present the theoretical analysis of the scheme. Numerical results demonstrate the high efficiency and accuracy of the method.

  • AMS Subject Headings

65M10, 78A48

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-12-791, author = {Dai , MiaoyuHuang , Zhongyi and Zhu , Wei}, title = {Convex Splitting Method for Strongly Anisotropic Solid-State Dewetting Problems in Two Dimensions}, journal = {East Asian Journal on Applied Mathematics}, year = {2022}, volume = {12}, number = {4}, pages = {791--820}, abstract = {

A novel sharp-interface model for the solid-state dewetting problem in the two-dimensional case is proposed. Instead of incorporating the Willmore energy or an $L_2$-curvature regularization term as is done in previous studies, we add an $L_1$-curvature regularization to the interfacial energy functional in order to make this problem well-posed. Experiments show that such regularization improves the computational efficiency. In strongly anisotropic case, we consider a new numerical scheme based on the convex-splitting idea. This approach remarkably relax the restriction on the time step. In addition, we present the theoretical analysis of the scheme. Numerical results demonstrate the high efficiency and accuracy of the method.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.261021.120122}, url = {http://global-sci.org/intro/article_detail/eajam/20885.html} }
TY - JOUR T1 - Convex Splitting Method for Strongly Anisotropic Solid-State Dewetting Problems in Two Dimensions AU - Dai , Miaoyu AU - Huang , Zhongyi AU - Zhu , Wei JO - East Asian Journal on Applied Mathematics VL - 4 SP - 791 EP - 820 PY - 2022 DA - 2022/08 SN - 12 DO - http://doi.org/10.4208/eajam.261021.120122 UR - https://global-sci.org/intro/article_detail/eajam/20885.html KW - Strongly anisotropic, convex-splitting, solid-state dewetting, parametric finite element method. AB -

A novel sharp-interface model for the solid-state dewetting problem in the two-dimensional case is proposed. Instead of incorporating the Willmore energy or an $L_2$-curvature regularization term as is done in previous studies, we add an $L_1$-curvature regularization to the interfacial energy functional in order to make this problem well-posed. Experiments show that such regularization improves the computational efficiency. In strongly anisotropic case, we consider a new numerical scheme based on the convex-splitting idea. This approach remarkably relax the restriction on the time step. In addition, we present the theoretical analysis of the scheme. Numerical results demonstrate the high efficiency and accuracy of the method.

Miaoyu Dai, Zhongyi Huang & Wei Zhu. (2022). Convex Splitting Method for Strongly Anisotropic Solid-State Dewetting Problems in Two Dimensions. East Asian Journal on Applied Mathematics. 12 (4). 791-820. doi:10.4208/eajam.261021.120122
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