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Volume 13, Issue 2
Computation of Two-Phase Biomembranes with Phase Dependent Material Parameters Using Surface Finite Elements

Charles M. Elliott & Björn Stinner

Commun. Comput. Phys., 13 (2013), pp. 325-360.

Published online: 2013-02

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  • Abstract

The shapes of vesicles formed by lipid bilayers with phase separation are governed by a bending energy with phase dependent material parameters together with a line energy associated with the phase interfaces. We present a numerical method to approximate solutions to the Euler-Lagrange equations featuring triangulated surfaces, isoparametric quadratic surface finite elements and the phase field approach for the phase separation. Furthermore, the method involves an iterative solution scheme that is based on a relaxation dynamics coupling a geometric evolution equation for the membrane surface with a surface Allen-Cahn equation. Remeshing and grid adaptivity are discussed, and in various simulations the influence of several physical parameters is investigated.

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@Article{CiCP-13-325, author = {}, title = {Computation of Two-Phase Biomembranes with Phase Dependent Material Parameters Using Surface Finite Elements}, journal = {Communications in Computational Physics}, year = {2013}, volume = {13}, number = {2}, pages = {325--360}, abstract = {

The shapes of vesicles formed by lipid bilayers with phase separation are governed by a bending energy with phase dependent material parameters together with a line energy associated with the phase interfaces. We present a numerical method to approximate solutions to the Euler-Lagrange equations featuring triangulated surfaces, isoparametric quadratic surface finite elements and the phase field approach for the phase separation. Furthermore, the method involves an iterative solution scheme that is based on a relaxation dynamics coupling a geometric evolution equation for the membrane surface with a surface Allen-Cahn equation. Remeshing and grid adaptivity are discussed, and in various simulations the influence of several physical parameters is investigated.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.170611.130112a}, url = {http://global-sci.org/intro/article_detail/cicp/7225.html} }
TY - JOUR T1 - Computation of Two-Phase Biomembranes with Phase Dependent Material Parameters Using Surface Finite Elements JO - Communications in Computational Physics VL - 2 SP - 325 EP - 360 PY - 2013 DA - 2013/02 SN - 13 DO - http://doi.org/10.4208/cicp.170611.130112a UR - https://global-sci.org/intro/article_detail/cicp/7225.html KW - AB -

The shapes of vesicles formed by lipid bilayers with phase separation are governed by a bending energy with phase dependent material parameters together with a line energy associated with the phase interfaces. We present a numerical method to approximate solutions to the Euler-Lagrange equations featuring triangulated surfaces, isoparametric quadratic surface finite elements and the phase field approach for the phase separation. Furthermore, the method involves an iterative solution scheme that is based on a relaxation dynamics coupling a geometric evolution equation for the membrane surface with a surface Allen-Cahn equation. Remeshing and grid adaptivity are discussed, and in various simulations the influence of several physical parameters is investigated.

Charles M. Elliott & Björn Stinner. (2020). Computation of Two-Phase Biomembranes with Phase Dependent Material Parameters Using Surface Finite Elements. Communications in Computational Physics. 13 (2). 325-360. doi:10.4208/cicp.170611.130112a
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