Speaker：JU, LILI，Department of Mathematics, University of South Carolina, Columbia,USA

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

Time：2015-12-18, 10:00-10:50am

Venue: Room 316 of Environment Building, Renmin University

 

Abstract：The Willmore flow formulated by phase field  elastic bending energy models 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 Willmore flow and the Willmore flow 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.In particular, we also incorporate novel linear operator splitting techniques into the numerical schemes to improve the discrete energy stability. In order to avoid the extra numerical instability brought by use of large penalty parameters in solving the constrained Willmore flow 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.