ORIGINAL PAPERS

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

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  • Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China

Received date: 2022-10-28

  Revised date: 2023-08-01

  Accepted date: 2023-08-04

  Online published: 2023-10-16

Supported by

The work of Leung was supported in part by the Hong Kong RGC 16302223.

Abstract

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.

Cite this article

Young Kyu Lee, Shingyu Leung . A Simple Embedding Method for the Laplace-Beltrami Eigenvalue Problem on Implicit Surfaces[J]. Communications on Applied Mathematics and Computation, 2024 , 6(2) : 1189 -1216 . DOI: 10.1007/s42967-023-00303-8

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