267616
20190913123103.0
doi
10.5075/epfl-MATHICSE-267616
REP_WORK
MATHICSE Technical Report : Biomembrane modeling with Isogeometric Analysis
Ã‰cublens
MATHICSE
2017-03
2017-03
18
Working Papers
MATHICSE Technical Report Nr. 06.2017
We consider the numerical approximation of lipid biomembranes, including red blood cells, described through the Canham-Helfrich model, according to which the shape minimizes the bending energy under area and volume constraints. Energy minimization is performed via L2- gradient flow of the Canham-Helfrich energy using two Lagrange multipliers to weakly enforce the constraints. This yields a highly nonlinear, high order, time dependent geometric Partial Differential Equation (PDE). We represent the biomembranes as single-patch NURBS closed surfaces. We discretize the geometric PDEs in space with NURBS-based Isogeometric Analysis and in time with Backward Differentiation Formulas. We tackle the nonlinearity in our formulation through a semi-implicit approach by extrapolating, at each time level, the geometric quantities of interest from previous time steps. We report the numerical results of the approximation of the Canham-Helfrich problem on ellipsoids of different aspect ratio, which lead to the classical biconcave shape of lipid vesicles at equilibrium. We show that this framework permits an accurate approximation of the Canham-Helfrich problem, while being computationally efficient.
Biomembrane
Canham-Helfrich energy
Geometric Partial Differential Equation
NURBS
Isogeometric Analysis
Backward Differentiation Formulas
Lagrange multipliers
247620
Bartezzaghi, Andrea
214528
245547
Dede', Luca
159570
240286
Quarteroni, Alfio
118377
MATHICSE-Group
2686136
http://infoscience.epfl.ch/record/267616/files/Report-06.2017_AB_LD_AQ.pdf
simone.deparis@epfl.ch
252102
Deparis, Simone
simone.deparis@epfl.ch
U10797
CMCS
Approved
oai:infoscience.epfl.ch:267616
DOI
working
julien.junod@epfl.ch
fantin.reichler@epfl.ch
EPFL
REP_WORK
overwrite