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.
| Identifer | oai:union.ndltd.org:CLAREMONT/oai:scholarship.claremont.edu:cgu_etd-1127 |
| Date | 01 January 2018 |
| Creators | Delengov, Vladimir |
| Publisher | Scholarship @ Claremont |
| Source Sets | Claremont Colleges |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | CGU Theses & Dissertations |
| Rights | © 2018 Vladimir Delengov, default |
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