A convolution thresholding scheme for the Willmore flow

被引：0

作者：

Grzhibovskis, Richards ^{[1
]}

Heintz, Alexei ^{[2
]}

机构：

[1] Univ Saarland, Dept Math, D-66123 Saarbrucken, Germany

[2] Chalmers, Dept Math, S-41296 Gothenburg, Sweden

来源：

INTERFACES AND FREE BOUNDARIES | 2008年 / 10卷 / 02期

关键词：

Willmore flow; convolution thresholding scheme;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A convolution thresholding approximation scheme for the Willmore geometric flow is constructed. It is based on an asymptotic expansion of the convolution of an indicator function with a smooth, isotropic kernel. The consistency of the method is justified when the evolving surface is smooth and embedded. Some aspects of the numerical implementation of the scheme are discussed and several numerical results are presented. Numerical experiments show that the method performs well even in the case of a non-smooth initial data.

引用

页码：139 / 153

页数：15

共 26 条

[1]

BENCE J, 1992, COMP CRYST GROW WORK, P73

[2] ON THE FAST FOURIER-TRANSFORM OF FUNCTIONS WITH SINGULARITIES [J].

BEYLKIN, G .

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 1995, 2 (04) :363-381

[3] MINIMUM ENERGY OF BENDING AS A POSSIBLE EXPLANATION OF BICONCAVE SHAPE OF HUMAN RED BLOOD CELL [J].

CANHAM, PB .

JOURNAL OF THEORETICAL BIOLOGY, 1970, 26 (01) :61-&

[4] A finite element method for surface restoration with smooth boundary conditions [J].

Clarenz, U ;

Diewald, U ;

Dziuk, G ;

Rumpf, M ;

Rusu, R .

COMPUTER AIDED GEOMETRIC DESIGN, 2004, 21 (05) :427-445

[5] RED BLOOD-CELL SHAPES AS EXPLAINED ON BASIS OF CURVATURE ELASTICITY [J].

DEULING, HJ ;

HELFRICH, W .

BIOPHYSICAL JOURNAL, 1976, 16 (08) :861-868

[6] A level set formulation for Willmore flow [J].

Droske, M ;

Rumpf, M .

INTERFACES AND FREE BOUNDARIES, 2004, 6 (03) :361-378

[7] Modeling the spontaneous curvature effects in static cell membrane deformations by a phase field formulation [J].

Du, Q ;

Liu, C ;

Ryham, R ;

Wang, X .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2005, 4 (03) :537-548

[8] A phase field formulation of the Willmore problem [J].

Du, Q ;

Liu, C ;

Ryham, R ;

Wang, XQ .

NONLINEARITY, 2005, 18 (03) :1249-1267

[9] A convolution-thresholding approximation of generalized curvature flows [J].

Grzhibovskis, R ;

Heintz, A .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2005, 42 (06) :2652-2670

[10]

GRZHIBOVSKIS R, 2004, 29 CHALM U TECH

← 1 2 3 →