Characterization of an adaptive refinement algorithm for a meshless eigenvalue solver based on radial basis functions

A meshless method based on a radial basis collocation approach is presented to calculate eigenvalues for the second-order wave equation. Instead of an explicit mesh topology only a node distribution is required to calculate electric fields, thus facilitating dynamic alteration of the discretization of an electromagnetic problem. An algorithm is presented that automatically adapts an initially very coarse discretization by adding points where higher accuracy is required by the physics of the problem. The algorithm is applied to a cylindrical cavity resonator and the rate of convergence is compared to uniform refinements with the radial basis method and to a regular grid-based finite-difference approach.