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arXiv · 2210.10982

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

Jackson C. Turner·Elena Cherkaev·Dong Wang
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Abstract

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.

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Jackson C. Turner, Elena Cherkaev, Dong Wang. 2022-10-20. A generalized expansion method for computing Laplace-Beltrami eigenfunctions on manifolds. https://arxiv.org/abs/2210.10982

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