Computing eigenmodes of elliptic operators using radial basis functions
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. Particular attention is given to the Laplacian operator in two dimensions, including techniques to avoid degradation of the solution near the boundaries. For regions with corner singularities, special functions must be added to the basis to maintain good convergence. Numerical results compare favorably to basic finite-element methods. (C) 2004 Elsevier Ltd. All rights reserved.
radial basis functions laplacian corner singularities eigenvalues numerical methods