A limited memory algorithm for bound constrained optimization
SIAM Journal on Scientific Computing
Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization
ACM Transactions on Mathematical Software (TOMS)
A phase field approach in the numerical study of the elastic bending energy for vesicle membranes
Journal of Computational Physics
Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions
Journal of Computational Physics
Finite element modeling of lipid bilayer membranes
Journal of Computational Physics
A phase field method for simulating morphological evolution of vesicles in electric fields
Journal of Computational Physics
Journal of Computational Physics
A phase field model for vesicle-substrate adhesion
Journal of Computational Physics
Modeling and computation of two phase geometric biomembranes using surface finite elements
Journal of Computational Physics
A fast algorithm for simulating vesicle flows in three dimensions
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.49 |
As two-dimensional fluid shells, lipid bilayer membranes resist bending and stretching but are unable to sustain shear stresses. This property gives membranes the ability to adopt dramatic shape changes. In this paper, a finite element model is developed to study static equilibrium mechanics of membranes. In particular, a viscous regularization method is proposed to stabilize tangential mesh deformations and improve the convergence rate of nonlinear solvers. The augmented Lagrangian method is used to enforce global constraints on area and volume during membrane deformations. As a validation of the method, equilibrium shapes for a shape-phase diagram of lipid bilayer vesicle are calculated. These numerical techniques are also shown to be useful for simulations of three-dimensional large deformation problems: the formation of tethers (long tube-like extensions); and Ginzburg-Landau phase separation of a two lipid-component vesicle. To deal with the large mesh distortions of the two-phase model, modification of viscous regularization is explored to achieve r-adaptive mesh optimization.