Computational parametric Willmore flow
Computational parametric Willmore flow
复制标题
DOI：
10.1007/s00211-008-0179-1
复制
发表时间：
2008-10
影响因子：
2.1
通讯作者：
G. Dziuk
中科院分区：
文献类型：
--
作者：
G. Dziuk
本文提出了一种计算Willmore流的新算法。这是Willmore泛函的L2梯度流，Willmore泛函是曲面的经典弯曲能。Willmore流描述的高度非线性系统的偏微分方程的四阶参数化的表面。空间离散的数值格式是稳定的和一致的。的离散化依赖于一个足够的计算的Willmore功能的第一变化与推导的第二变化的面积泛函，这是非常适合于离散化技术与有限元。该算法在曲面上使用有限元。给出了分段线性有限元的数值算例和检验。完整算法的收敛性证明仍然是一个悬而未决的问题。
We propose a new algorithm for the computation of Willmore flow. This is theL2-gradient flow for the Willmore functional, which is the classical bending energy of a surface. Willmore flow is described by a highly nonlinear system of PDEs of fourth order for the parametrization of the surface. The spatially discrete numerical scheme is stable and consistent. The discretization relies on an adequate calculation of the first variation of the Willmore functional together with a derivation of the second variation of the area functional which is well adapted to discretization techniques with finite elements. The algorithm uses finite elements on surfaces. We give numerical examples and tests for piecewise linear finite elements. A convergence proof for the full algorithm remains an open question.