A generalized expansion method for computing Laplace-Beltrami eigenfunctions on manifolds

Autor:	Turner, Jackson C., Cherkaev, Elena, Wang, Dong
Rok vydání:	2022
Předmět:	Mathematics - Numerical Analysis Mathematical Physics 65N25m 47A70 65N85 35J05
Druh dokumentu:	Working Paper
Popis:	Eigendecomposition of the Laplace-Beltrami operator is instrumental for a variety of applications from physics to data science. We develop a numerical method of computation of the eigenvalues and eigenfunctions of the Laplace-Beltrami operator on a smooth bounded domain based on the relaxation to the Schr\"odinger operator with finite potential on a Riemannian manifold and projection in a special basis. We prove spectral exactness of the method and provide examples of calculated results and applications, particularly, in quantum billiards on manifolds. Comment: 17 pages, 13 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2210.10982 Zobrazit plný text záznamu View this record from Arxiv