Abstract
This paper presents a phase-field model for simulating the three-dimensional deformation of vesicle membranes, incorporating area-difference elasticity (i.e., the elasticity arising from the difference between the inner and outer lipid leaflets), with constraints on bulk volume and surface area. We develop efficient numerical schemes based on the Fourier-spectral method for spatial discretization and temporal evolution. The model successfully captures a wide variety of steady-state vesicle shapes. The numerical experiments demonstrate that by tuning the simulation parameters, the vesicle can transition from a simple spherical and discocyte shape to complete membrane fission, asymmetric pear shaped structures, as well as complex multi-armed starfish-like and nested configuration. These results highlight the crucial role of area-difference elasticity in determining vesicle morphology.