Computing Eigenmodes of Elliptic Operators on Manifolds Using Radial Basis Functions

<p>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.</p>

Name thesis:degree_name

Mathematics, PhD

Level thesis:degree_level

Open Access Dissertation

Discipline thesis:degree_discipline

School of Mathematical Sciences

Year dc:date.available

2018

Author dc:creator

• Delengov, Vladimir

Contributors dc:contributor

• Chiu-Yen Kao
• Marina Chugunova
• Ali Nadim

• radial basis functions
• Laplace-Beltrami operator
• eigenproblem
• meshfree
• elliptic operators
• manifold
• Numerical Analysis and Computation
• Partial Differential Equations

Repository record dc:identifier

https://scholarship.claremont.edu/cgu_etd/113

OAI identifier oai:identifier

oai:scholarship.claremont.edu:cgu_etd-1127