A Simple Embedding Method for the Laplace-Beltrami Eigenvalue Problem onImplicit Surfaces  

作　　者：Young Kyu Lee Shingyu Leung 

机构地区：[1]Department of Mathematics,The Hong Kong University of Science and Technology,Clear Water Bay,Hong Kong,China

出　　处：《Communications on Applied Mathematics and Computation》2024年第2期1189-1216,共28页应用数学与计算数学学报（英文）

基　　金：supported in part by the Hong Kong RGC 16302223.

摘　　要：We propose a simple embedding method for computing the eigenvalues and eigenfunctions of the Laplace-Beltrami operator on implicit surfaces.The approach follows an embedding approach for solving the surface eikonal equation.We replace the differential operator on the interface with a typical Cartesian differential operator in the surface neighborhood.Our proposed algorithm is easy to implement and efficient.We will give some two-and three-dimensional numerical examples to demonstrate the effectiveness of our proposed approach.

关 键 词：Laplace-Beltrami operator Level set method Implicit representation EIGENVALUES Numerical PDEs 

分 类 号：O17[理学—数学]