Title:  Efficient and Stable Exponential Time Differencing Runge-Kutta Methods for Phase Field Elastic Bending Energy Models

Abstract: The Willmore flow formulated by phase field dynamics based on the elastic bending energy model has been widely used to describe the shape transformation of biological lipid vesicles. In this talk, we present some efficient and stable numerical methods for simulating the unconstrained phase field Willmore dynamics and the phase field Willmore dynamics with fixed volume and surface area constraints. The proposed methods can be high-order accurate and are completely explicit in nature, by combining exponential time differencing Runge-Kutta approximations for time integration with spectral discretizations for spatial operators on regular meshes. We also incorporate novel linear operator splitting techniques into the numerical schemes to improve the discrete energy stability. In order to avoid extra numerical instability brought by use of large penalty parameters in solving the constrained phase field Willmore dynamics problem, a modified  augmented Lagrange multiplier approach is proposed and adopted. Various numerical experiments are performed to demonstrate accuracy and stability of the proposed methods.

报告人简介：鞠立力，南卡罗来纳大学数学系教授，Associate Editor of SIAM Journal on Numerical Analysis。主持多项NSF、DoE基金。已在国际著名刊物如： SIAM Journal on Scientific Computing, SIAM Journal on Numerical Analysis, Computer Methods in Applied Mechanics and Engineering, Mathematics of Computation, Journal of Computational Physics等杂志上发表数十篇学术论文.

报告时间：2017年10月12日（周四）上午9:30-10:30

报告地点：长清湖校区B434报告厅

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