Date of Award
Honors College Thesis
Two localized meshless methods with radial basis functions are considered for solving eigenvalue problems on two different domains, i.e., a L-shaped domain and an irregular domain. The irregular domain used in this study comes from an application of the eigenvalue problem as it plays a role in the reconstruction of velocity vector fields. This study finds that both localized Kansa’s method and the Localized Method of Approximate Particular Solutions provide a good numerical approximation to the solution of the eigenvalue problem. Through numerical experiments, a good value for the shape parameter can be determined for each domain for each method which will minimize the relative error and maximum relative error in the eigenvalues of the numeric approximation. The relative error and maximum relative error were calculated for each domain using different grid sizes. In addition, the convergence rates for both methods were determined for both domains, and appear to be quite similar.
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Kern, Amy M., "Localized Meshless Methods With Radial Basis Functions For Eigenvalue Problems" (2013). Honors Theses. 176.