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Computing the dynamics of biomembranes by combining conservative level set and adaptive finite element methods

Aymen Laadhari, Pierre Saramito, Chaouqi Misbah
Journal of Computational Physics
Vol. 263, pp. 328–352, 2014


In this letter, we present a computational framework based on the use of the Newton and level set methods and tailored for the modeling of bubbles with surface tension in a surrounding Newtonian fluid. We describe a fully implicit and monolithic finite element method that maintains stability for significantly larger time steps compared to the usual explicit method and features substantial computational savings. A suitable transformation avoids the introduction of an additional mixed variable in the variational problem. An exact tangent problem is derived and the nonlinear problem is solved by a quadratically convergent Newton method. In addition, we consider a generalization to the multidimensional case of the Kou’s and McDougall’s methods, resulting in a faster convergence. The method is benchmarked against known results with the aim of illustrating its accuracy and robustness.

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  author = {Aymen Laadhari and Pierre Saramito and Chaouqi Misbah},
  title = {Computing the dynamics of biomembranes by combining conservative level set and adaptive finite element methods},
  journal = {Journal of Computational Physics},
  year = {2014},
  month = {},
  pages = {328–352},
  volume = {263},
  number = {},
  keywords = {Level set methodMass conservationAdaptive finite element method, Helfrich energy, Vesicle dynamics, Fluid mechanics}