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

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.

Keywords

Laplace-Beltrami operator / Level set method / Implicit representation / Eigenvalues / Numerical PDEs

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Funding

University Grants Committee(16302223)