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Full-Text Articles in Numerical Analysis and Computation
Computing Eigenmodes Of Elliptic Operators On Manifolds Using Radial Basis Functions, Vladimir Delengov
Computing Eigenmodes Of Elliptic Operators On Manifolds Using Radial Basis Functions, Vladimir Delengov
CGU Theses & Dissertations
In this work, a numerical approach based on meshless methods is proposed to obtain eigenmodes of Laplace-Beltrami operator on manifolds, and its performance is compared against existing alternative methods. Radial Basis Function (RBF)-based methods allow one to obtain interpolation and differentiation matrices easily by using scattered data points. We derive expressions for such matrices for the Laplace-Beltrami operator via so-called Reilly’s formulas and use them to solve the respective eigenvalue problem. Numerical studies of proposed methods are performed in order to demonstrate convergence on simple examples of one-dimensional curves and two-dimensional surfaces.