Numerical shape optimization of the Canham-Helfrich-Evans bending energy
From MaRDI portal
Publication:6162885
DOI10.1016/j.jcp.2023.112218arXiv2107.13794OpenAlexW3186636676MaRDI QIDQ6162885
Kevin Sturm, Joachim Schöberl, Michael Neunteufel
Publication date: 16 June 2023
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2107.13794
shape optimizationmixed finite element methodbiomembranedistributional curvatureCanham-Helfrich-Evans bending energy
Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Manifolds and measure-geometric topics (49Qxx)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Computing the dynamics of biomembranes by combining conservative level set and adaptive finite element methods
- 3D numerical simulations of vesicle and inextensible capsule dynamics
- Global minimizers for the doubly-constrained Helfrich energy: the axisymmetric case
- Comparison between advected-field and level-set methods in the study of vesicle dynamics
- A fast algorithm for simulating vesicle flows in three dimensions
- 3D vesicle dynamics simulations with a linearly triangulated surface
- An immersed boundary method for simulating vesicle dynamics in three dimensions
- Discrete quadratic curvature energies
- An algorithm for evolutionary surfaces
- Viscous regularization and r-adaptive remeshing for finite element analysis of lipid membrane mechanics
- Computational parametric Willmore flow
- Parametric FEM for geometric biomembranes
- Uniform convergence of discrete curvatures from nets of curvature lines
- On the equilibrium equation for a generalized biological membrane energy by using a shape optimization approach
- NETGEN: An advancing front 2D/3D-mesh generator based on abstract rules
- A stabilized finite element formulation for liquid shells and its application to lipid bilayers
- A phase field approach in the numerical study of the elastic bending energy for vesicle membranes
- A Convergent evolving finite element algorithm for Willmore flow of closed surfaces
- Bending models of lipid bilayer membranes: spontaneous curvature and area-difference elasticity
- Existence of varifold minimizers for the multiphase Canham-Helfrich functional
- A convergent evolving finite element algorithm for mean curvature flow of closed surfaces
- An algorithm for the elastic flow of surfaces
- Higher Order Triangular Finite Elements with Mass Lumping for the Wave Equation
- Distributed shape derivativeviaaveraged adjoint method and applications
- First variation of the general curvature-dependent surface energy
- Geometrically Consistent Mesh Modification
- Shapes and Geometries
- TANGENTIAL-DISPLACEMENT AND NORMAL–NORMAL-STRESS CONTINUOUS MIXED FINITE ELEMENTS FOR ELASTICITY
- Efficient PDE Constrained Shape Optimization Based on Steklov--Poincaré-Type Metrics
- The Shapes of Things
- Higher-Order Finite Element Methods and Pointwise Error Estimates for Elliptic Problems on Surfaces
- Optimal Isoparametric Finite Elements and Error Estimates for Domains Involving Curved Boundaries
- The Hellan-Herrmann-Johnson Method: Some New Error Estimates and Postprocessing
- Boundary Integral and Singularity Methods for Linearized Viscous Flow
- Two-Dimensional Shape Optimization with Nearly Conformal Transformations
- A stabilized finite element method for the Stokes problem based on polynomial pressure projections
- Nonlinear Conjugate Gradient Methods for PDE Constrained Shape Optimization Based on Steklov--Poincaré-Type Metrics
- Parametric Approximation of Willmore Flow and Related Geometric Evolution Equations
- Modelling fluid deformable surfaces with an emphasis on biological interfaces
- Mathematics of Surfaces XI
- Global minimizers for axisymmetric multiphase membranes
- Finite element methods for surface PDEs
