Efficient and stable exponential time differencing Runge-Kutta methods for phase field elastic bending energy models

JOURNAL OF COMPUTATIONAL PHYSICS

卷:316

Article

Wang, Xiaoqiang¹  Ju, Lili²  Du, Qiang³ 

[1] Florida State Univ, Dept Comp Sci, Tallahassee, FL 32306 USA

[2] Univ S Carolina, Dept Math, Columbia, SC 29208 USA

[3] Columbia Univ, Dept Appl Phys & Appl Math, New York, NY 10027 USA

关键词: Elastic bending energy;    Willmore flow;    Phase field method;    Exponential time differencing;    Runge-Kutta methods;    Augmented Lagrange multiplier;   

DOI  :  10.1016/j.jcp.2016.04.004

来源: Elsevier

【 摘 要 】

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 paper, we develop and investigate 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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free