Parametric FEM for geometric biomembranes

  • Authors:

  • Andrea Bonito;Ricardo H. Nochetto;M. Sebastian Pauletti

  • Affiliations:

  • Department of Mathematics, Texas A&M University, College Station, TX 77843, USA;Department of Mathematics, University of Maryland, College Park, MD 20742, USA and Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA;Department of Mathematics, Texas A&M University, College Station, TX 77843, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2010

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Abstract

We consider geometric biomembranes governed by an L^2-gradient flow for bending energy subject to area and volume constraints (Helfrich model). We give a concise derivation of a novel vector formulation, based on shape differential calculus, and corresponding discretization via parametric FEM using quadratic isoparametric elements and a semi-implicit Euler method. We document the performance of the new parametric FEM with a number of simulations leading to dumbbell, red blood cell and toroidal equilibrium shapes while exhibiting large deformations.