## Computing Eigenmodes of Elliptical Operators Using Radial Basis Functions

2003-03-21
##### Authors
Platte, Rodrigo B.
Driscoll, Tobin A.
##### 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.
##### Keywords
radial basis functions , eigenvalues , elliptic operators , numerical methods , Laplacian