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AN ENERGY-STABLE PARAMETRICFINITE ELEMENT METHOD FOR SIMULATING solid-state dewetting PROBLEMS INTHREE DIMENSIONS

Journal of Computational Mathematics 2023年第4期41卷 771-796页

作者： Weizhu Bao Quan Zhao Department of Mathematics National University of SingaporeSingapore119076

We propose an accurate and energy-stable parametric finite element method for solving the sharp-interface continuum model of solid-state dewetting in three-dimensional space.The model describes the motion of the film/vapor interface with contact line migration and is governed by the surface diffusion equation with proper boundary conditions at the contact line.We present a weak formulation for the problem,in which the contact angle condition is weakly enforced.By using piecewise linear elements in space and backward Euler method in time,we then discretize the formulation to obtain a parametric finite element approximation,where the interface and its contact line are evolved simultaneously.The resulting numerical method is shown to be well-posed and unconditionally energystable.Furthermore,the numerical method is generalized to the case of anisotropic surface energies in the Riemannian metric form.Numerical results are reported to show the convergence and efficiency of the proposed numerical method as well as the anisotropic effects on the morphological evolution of thin films in solid-state dewetting.

关键词： solid-state dewetting Surface diffusion Contact line migration Contact angle Parametric finite element method Anisotropic surface energy

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EFFICIENT LINEAR SCHEMES WITH UNCONDITIONAL ENERGY STABILITY FOR THE PHASE FIELD MODEL OF solid-state dewetting PROBLEMS

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Journal of Computational Mathematics 2020年第3期38卷 452-468页

作者： Jie Chen Zhengkang He Shuyu Sun Shimin Guo Zhangxin Chen School of Mathematics and Statistics Xi'an Jiaotong UniversityXi'an 710049China Computational Transport Phenomena Laboratory Division of Physical Science and EngineeringKing Abdullah University of Science and TechnologyThuwal 23955-6900Kingdom of Saudi Arabia School of Mathematics and Statistics Xi'an Jiaotong Universityy Xi'an 710049China Department of Chemical&Petroleum Engineering Schulich School of EngineeringUniversity of Calgary2500 University Drive N.W.CalgaryAlberta T2N 1N4Canada

In this paper,we study linearly first and second order in time,uniquely solvable and unconditionally energy stable numerical schemes to approximate the phase field model of solid-state dewetting problems based on the novel"scalar auxiliary variable"(SAV)approach,a new developed efficient and accurate method for a large class of gradient flows.The schemes are based on the first order Euler method and the second order backward differential formulas(BDF2)for time discretization,and finite element methods for space discretization.The proposed schemes are proved to be unconditionally stable and the discrete equations are uniquely solvable for all time steps.Various numerical experiments are presented to validate the stability and accuracy of the proposed schemes.

关键词： Phase field models solid-state dewetting SAV Energy stability Surface diffusion Finite element method

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