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

10/20/2022

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by   Jackson C. Turner, et al.

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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 Schrödinger 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.