A Novel Variational Meshless Method With Radial Basis Functions for Waveguide Eigenvalue Problems

A novel variational meshless method is presented to calculate a large number of modes of a homogeneous waveguide with an arbitrary shape. The proposed technique is based on the variational principle combined with the meshless method using radial basis functions (RBFs). Compared with the more traditional point-matching meshless method with RBFs, the proposed technique leads to a well-conditioned matrix problem, and no preconditioning is needed. An iterative refinement algorithm is also presented, which generates automatically new collocation points and locally defined shape parameters for the RBFs, until a prescribed convergence is reached. As proved through many examples, including waveguides with sharp corners, the variational meshless method permits to calculate a large number of waveguide modes with high precision in a very short computing time.