A Simple Embedding Method for the Laplace-Beltrami Eigenvalue Problem on Implicit Surfaces
Young Kyu Lee, Shingyu Leung
Communications on Applied Mathematics and Computation ›› 2023, Vol. 6 ›› Issue (2) : 1189-1216.
A Simple Embedding Method for the Laplace-Beltrami Eigenvalue Problem on Implicit Surfaces
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.
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