Eigenmodes of Isospectral Drums
SIAM Review
Applied Mathematics and Computation
Spectral methods in MATLAB
Eigenfrequencies of fractal drums
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Bounds to eigenvalues of the Laplacian on L-shaped domain by variational methods
Journal of Computational and Applied Mathematics
Eigenvalue stability of radial basis function discretizations for time-dependent problems
Computers & Mathematics with Applications
Application of the RBF meshless method to the solution of the radiative transport equation
Journal of Computational Physics
Applied Numerical Mathematics
Hi-index | 0.09 |
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.