000267616 001__ 267616
000267616 005__ 20190913123103.0
000267616 0247_ $$2doi$$a10.5075/epfl-MATHICSE-267616
000267616 037__ $$aREP_WORK
000267616 245__ $$aMATHICSE Technical Report : Biomembrane modeling with Isogeometric Analysis
000267616 260__ $$aÉcublens$$bMATHICSE$$c2017-03
000267616 269__ $$a2017-03
000267616 300__ $$a18
000267616 336__ $$aWorking Papers
000267616 500__ $$aMATHICSE Technical Report Nr. 06.2017
000267616 520__ $$aWe 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.
000267616 6531_ $$aBiomembrane
000267616 6531_ $$aCanham-Helfrich energy
000267616 6531_ $$aGeometric Partial Differential Equation
000267616 6531_ $$aNURBS
000267616 6531_ $$aIsogeometric Analysis
000267616 6531_ $$aBackward Differentiation Formulas
000267616 6531_ $$aLagrange multipliers
000267616 700__ $$0247620$$aBartezzaghi, Andrea$$g214528
000267616 700__ $$0245547$$aDede', Luca$$g159570
000267616 700__ $$0240286$$aQuarteroni, Alfio$$g118377
000267616 710__ $$aMATHICSE-Group
000267616 8560_ $$fsimone.deparis@epfl.ch
000267616 8564_ $$uhttps://infoscience.epfl.ch/record/267616/files/Report-06.2017_AB_LD_AQ.pdf$$s2686136
000267616 909C0 $$yApproved$$pCMCS$$xU10797$$msimone.deparis@epfl.ch$$zDeparis, Simone$$0252102
000267616 909CO $$pDOI$$ooai:infoscience.epfl.ch:267616$$pworking
000267616 960__ $$ajulien.junod@epfl.ch
000267616 961__ $$afantin.reichler@epfl.ch
000267616 973__ $$aEPFL
000267616 980__ $$aREP_WORK
000267616 981__ $$aoverwrite