论文标题
一种用于计算歧管上laplace-beltrami特征函数的广义扩展方法
A generalized expansion method for computing Laplace-Beltrami eigenfunctions on manifolds
论文作者
论文摘要
Laplace-Beltrami操作员的特征分类对从物理学到数据科学的各种应用都有帮助。我们开发了一种基于平滑限制的域上的Laplace-Beltrami操作员的特征值和本征函数计算的数值方法，该方法基于对Schrödinger操作员的放松，在特殊基础上具有有限的Riemannian歧管和投影。我们证明了该方法的光谱精确性，并提供了计算出的结果和应用的示例，特别是在量子台球中。
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.
