论文标题
与分析溶液相比，具有基于晶格的近似值的表面特征值
Surface Eigenvalues with Lattice-Based Approximation In comparison with analytical solution
论文作者
论文摘要
在本文中，我们提出了一种无网格的方法来计算嵌入$ \ Mathbb r^3 $的给定表面的特征值和特征函数。我们将点云数据用作输入，并为表面某些邻域生成晶格近似。我们计算了立方晶格图的特征值和特征值，作为表面上拉普拉斯 - 贝特拉米操作员的特征值和特征函数的近似值。我们在具有各种拓扑的表面上执行了广泛的数值实验，并比较了从点云表面与精确的解决方案和使用三角形网格的标准有限元方法进行比较。
In this paper, we propose a meshless method of computing eigenvalues and eigenfunctions of a given surface embedded in $\mathbb R^3$. We use point cloud data as input and generate the lattice approximation for some neighborhood of the surface. We compute the eigenvalues and eigenvectors of the cubic lattice graph as an approximation of the eigenvalues and eigenfunctions of the Laplace-Beltrami operator on the surface. We perform extensive numerical experiments on surfaces with various topology and compare our computed eigenvalues from point cloud surface with exact solutions and standard finite element methods using triangle mesh.
