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A hybrid numerical method for the phase‐field model of fluid vesicles in three‐dimensional space

We propose an accurate and robust numerical method for the phase‐field model of fluid vesicles. An equilibrium shape of fluid vesicle is obtained by minimizing the bending energy with volume and surface area constraints. We propose a hybrid numerical scheme that combines the Lagrange multiplier and penalty methods for two constraints. The numerical method is based on a nonlinearly stabilized splitting scheme and a direct volume correction algorithm. A large penalty constant is generally required; however, it does not guarantee that the surface area converges to a given value. Thus, we propose an adaptive constraint algorithm for the penalty method. Various numerical examples are performed to demonstrate the accuracy and robustness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.