Convergence of discrete Laplace-Beltrami operators over surfaces
Convergence of discrete Laplace-Beltrami operators over surfaces
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DOI：
10.1016/j.camwa.2004.05.001
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发表时间：
2004-08
影响因子：
2.9
通讯作者：
Guoliang Xu
中科院分区：
文献类型：
--
作者：
Guoliang Xu
离散Laplace-Beltrami算子的收敛性是分析涉及该算子的某些几何偏微分方程数值模拟过程收敛性的基础。本文的目的是回顾几个已经使用的离散Laplace-Beltrami算子在三角曲面和研究数值，以及理论上，它们的收敛行为。我们表明，没有一个是收敛的，但其中两个，提出了Desbrun等人。和Meyer等人，在特殊情况下收敛。我们指出这种特殊情况在几何偏微分方程的数值模拟中是非常重要的。
The convergence property of the discrete Laplace-Beltrami operator is the foundationof convergence analysis of the numerical simulation process of some geometric partial differential equations which involve the operator. The aim of this paper is to review several already-used discrete Laplace-Beltrami operators over triangulated surface and study numerically, as well as theoretically, their convergent behavior. We show that none of them is convergent in general, but two of them, proposed by Desbrun et al. and Meyer et al., are convergent in a special case. We point out that this special case is very important in the numerical simulation of geometric partial differential equations.