Close Search Advanced
Journals
Resources
About Us
Open Access

An Efficient and Unconditionally Energy Stable Scheme for Simulating Solid-State Dewetting of Thin Films with Isotropic Surface Energy

An Efficient and Unconditionally Energy Stable Scheme for Simulating Solid-State Dewetting of Thin Films with Isotropic Surface Energy
Preview
Add to basket

Year:    2019

Author:    Qiong-Ao Huang, Wei Jiang, Jerry Zhijian Yang

Communications in Computational Physics, Vol. 26 (2019), Iss. 5 : pp. 1444–1470

Abstract

In this paper, we propose highly efficient, unconditionally energy-stable numerical schemes to approximate the isotropic phase field model of solid-state dewetting problems by using the invariant energy quadratization (IEQ) method. The phase field model is governed by the isotropic Cahn-Hilliard equation with degenerate mobilities and dynamic contact line boundary conditions. By using the backward differential formula to discretize temporal derivatives, we construct linearly first- and second-order IEQ schemes for solving the model. It can be rigorously proved that these numerical schemes are unconditionally energy-stable and satisfy the total mass conservation during the evolution. By performing numerical simulations, we demonstrate that these IEQ-based schemes (including the first-order IEQ/BDF1, second-order IEQ/BDF2) are highly efficient, accurate and energy-stable. Furthermore, many interesting dewetting phenomena (such as the hole dynamics, pinch-off), are investigated by using the proposed IEQ schemes.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.2019.js60.07

Communications in Computational Physics, Vol. 26 (2019), Iss. 5 : pp. 1444–1470

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:    Solid-state dewetting surface diffusion phase-field model degenerate Cahn-Hilliard equation invariant energy quadratization unconditionally energy-stable.

Author Details

Qiong-Ao Huang

Wei Jiang

Jerry Zhijian Yang

  1. A computationally optimal relaxed scalar auxiliary variable approach for solving gradient flow systems

    Huang, Qiong-Ao | Yuan, Cheng | Zhang, Gengen | Zhang, Lian

    Computers & Mathematics with Applications, Vol. 156 (2024), Iss. P.64

    https://doi.org/10.1016/j.camwa.2023.12.017 [Citations: 1]

  2. Fully-discrete energy-preserving scheme for the space-fractional Klein–Gordon equation via Lagrange multiplier type scalar auxiliary variable approach

    Huang, Qiong-Ao | Zhang, Gengen | Wu, Bing

    Mathematics and Computers in Simulation, Vol. 192 (2022), Iss. P.265

    https://doi.org/10.1016/j.matcom.2021.09.002 [Citations: 4]

  3. A Regularized Model for Wetting/Dewetting Problems: Positivity and Asymptotic Analysis

    Zhou, Zeyu | Jiang, Wei | Zhang, Zhen

    Journal of Nonlinear Science, Vol. 34 (2024), Iss. 3

    https://doi.org/10.1007/s00332-024-10020-y [Citations: 0]

  4. A Structure-Preserving, Upwind-SAV Scheme for the Degenerate Cahn–Hilliard Equation with Applications to Simulating Surface Diffusion

    Huang, Qiong-Ao | Jiang, Wei | Yang, Jerry Zhijian | Yuan, Cheng

    Journal of Scientific Computing, Vol. 97 (2023), Iss. 3

    https://doi.org/10.1007/s10915-023-02380-6 [Citations: 5]

  5. A $$\theta $$-L Approach for the Simulation of Solid-State Dewetting Problems with Strongly Anisotropic Surface Energies

    Huang, Weijie | Jiang, Wei | Wang, Yan

    Journal of Scientific Computing, Vol. 100 (2024), Iss. 2

    https://doi.org/10.1007/s10915-024-02589-z [Citations: 0]

  6. A family of effective structure-preserving schemes with second-order accuracy for the undamped sine–Gordon equation

    Wang, Jun-Ya | Huang, Qiong-Ao

    Computers & Mathematics with Applications, Vol. 90 (2021), Iss. P.38

    https://doi.org/10.1016/j.camwa.2021.03.009 [Citations: 8]

  7. Linear multi-step methods and their numerical stability for solving gradient flow equations

    Huang, Qiong-Ao | Jiang, Wei | Yang, Jerry Zhijian | Zhang, Gengen

    Advances in Computational Mathematics, Vol. 49 (2023), Iss. 3

    https://doi.org/10.1007/s10444-023-10043-1 [Citations: 4]

  8. An energy stable finite difference method for anisotropic surface diffusion on closed curves

    Lai, Ming-Chih | Park, Sangbeom | Seol, Yunchang

    Applied Mathematics Letters, Vol. 127 (2022), Iss. P.107848

    https://doi.org/10.1016/j.aml.2021.107848 [Citations: 2]

  9. A Diffuse-Interface Approach for Solid-State Dewetting with Anisotropic Surface Energies

    Garcke, Harald | Knopf, Patrik | Nürnberg, Robert | Zhao, Quan

    Journal of Nonlinear Science, Vol. 33 (2023), Iss. 2

    https://doi.org/10.1007/s00332-023-09889-y [Citations: 6]

  10. A Parametric Finite Element Method for Solid-State Dewetting Problems in Three Dimensions

    Zhao, Quan | Jiang, Wei | Bao, Weizhu

    SIAM Journal on Scientific Computing, Vol. 42 (2020), Iss. 1 P.B327

    https://doi.org/10.1137/19M1281666 [Citations: 26]

  11. Structure Preserving Primal Dual Methods for Gradient Flows with Nonlinear Mobility Transport Distances

    Carrillo, José A. | Wang, Li | Wei, Chaozhen

    SIAM Journal on Numerical Analysis, Vol. 62 (2024), Iss. 1 P.376

    https://doi.org/10.1137/23M1562068 [Citations: 1]

  12. An energy-stable parametric finite element method for simulating solid-state dewetting

    Zhao, Quan | Jiang, Wei | Bao, Weizhu

    IMA Journal of Numerical Analysis, Vol. 41 (2021), Iss. 3 P.2026

    https://doi.org/10.1093/imanum/draa070 [Citations: 18]