期刊
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
卷 315, 期 -, 页码 691-712出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2016.10.041
关键词
Phase field; Allen-Cahn; Linear; Elastic bending energy; Invariant energy quadratization; Energy stability
资金
- U.S. National Science Foundation [DMS-1200487, DMS-1418898, DMS-1521965]
- U.S. Department of Energy [DE-SC0008087-ER6539]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1418898] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1200487, 1521965] Funding Source: National Science Foundation
In this paper, we study efficient numerical schemes of the classical phase field elastic bending energy model that has been widely used to describe the shape deformation of biological lipid vesicles, in which the free energy of the system consists of an elastic bending energy, a surface area constraint and a volume constraint. One major challenge in solving such model numerically is how to design appropriate temporal discretizations in order to preserve energy stability with large time step sizes at the semi-discrete level. We develop a first order and a second order time stepping scheme for this highly nonlinear and stiff parabolic PDE system based on the Invariant Energy Quadratization approach. In particular, the resulted semi-discretizations lead to linear systems in space with symmetric positive definite operators at each time step, thus can be efficiently solved. In addition, the proposed schemes are rigorously proved to be unconditionally energy stable. Various numerical experiments in 2D and 3D are presented to demonstrate the stability and accuracy of the proposed schemes. (C) 2016 Elsevier B.V. All rights reserved.
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