Computing Eigenmodes of Elliptical Operators Using Radial Basis Functions
Date
2003-03-21
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Department of Mathematical Sciences
Abstract
Radial basis function (RBF) approximations have been successfully
used to solve boundary-value problems numerically. We show that RBFs
can also be used to compute eigenmodes of elliptic operators. Special
attention is given to the Laplacian operator in two dimensions. We include
techniques to avoid degradation of the solution near the boundaries and
corner singularities. Numerical results compare favorably to basic finite
element methods.
Description
Keywords
radial basis functions, eigenvalues, elliptic operators, numerical methods, Laplacian