Computation of Two-Phase Biomembranes with Phase Dependent Material Parameters Using Surface Finite Elements (Communications in Computational Physics, 2018)
The shapes of vesicles formed by lipid bilayers with phase separation aregoverned by a bending energy with phase dependent material parameters togetherwith a line energy associated with the phase interfaces. We present a numerical methodto approximate solutions to the Euler-Lagrange equations featuring triangulated surfaces, isoparametric quadratic surface finite elements and the phase field approach forthe phase separation. Furthermore, the method involves an iterative solution schemethat is based on a relaxation dynamics coupling a geometric evolution equation for themembrane 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.