SSE Talk | 下周讲座预告
Dear all,
You are cordially invited to an academic seminar to be delivered by Prof.Zhen ZHANG on November 2 (Thursday). Please find the details as follows.
Seminar Information
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Topic: An Operator-splitting Optimization Approach for Phase-field Simulation of Equilibrium Shapes of Crystals
Time & Date: 4:00-5:00 PM, November 2 (Thursday)
Venue: Room 108, Teaching D
Speaker: Prof. Zhen ZHANG, Southern University of Science and Technology
Host: Prof. Dongdong HE, The Chinese University of Hong Kong, Shenzhen
Language: Chinese
Abstract:
Computing equilibrium shapes of crystals (ESC) is a challenging problem in materials science that involves minimizing an orientation-dependent (i.e., anisotropic) surface energy functional subject to a prescribed mass constraint. The highly nonlinear and singular anisotropic terms in the problem make it very challenging from both the analytical and numerical aspects. Especially, when the anisotropic strength is very large (i.e., strongly anisotropic cases), the ESC will form some singular, sharp corners even if the surface energy function is smooth. Traditional numerical approaches, such as the $H^{-1}$ gradient flow, are unable to produce true sharp corners due to the necessary addition of a high-order regularization term that penalizes sharp corners and rounds them off. In this paper, we propose a new numerical method based on the Davis-Yin splitting (DYS) optimization algorithm to predict the ESC instead of using gradient flow approaches. We discretize the infinite-dimensional phase-field energy functional in the absence of regularization terms and transform it into a finite-dimensional constraint minimization problem. The resulting optimization problem is solved using the DYS method which automatically guarantees the mass conservation and bound-preserving properties. We also prove the global convergence of the proposed algorithm. These desired properties are numerically observed. In particular, the proposed method can produce real sharp corners with satisfying accuracy. Finally, we present numerous numerical results to demonstrate that the ESC can be well simulated under different anisotropies in surface energies, confirming the effectiveness and efficiency of the proposed method.
Biography
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Prof. Zhen ZHANG is an associate Professor at Department of Mathematics, Southern University of Science and Technology, China. His research interests include numerical PDEs, multiphase complex fluid problems and high-dimensional data analysis. He received the B.S. degree in Mathematics from University of Science and Technology of China in 2007, and Ph.D. degree in Applied Mathematics from The Hong Kong University of Science and Technology in 2013. He worked as a postdoctoral fellow at Department of Mathematics in National University of Singapore from 2013 to 2015. He joined Southern University of Science and Technology in 2015.
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