A Comparison of Three Meshless Algorithms: Radial Point Interpolation, Non-Symmetric and Symmetric Kansa MethodThe Meshless Radial Point Interpolation Method for Time-Domain Electromagnetics

Abstract—Three different meshless methods based on radial basis functions are investigated for the numerical solution of electromagnetic eigenvalue problems. The three algorithms, the non-symmetric Kansa approach, the symmetric Kansa method and the radial point interpolation method, are first described putting emphasis on the influence of their formalism on practical implementation. The convergence rate of these meshless methods is then investigated, showing through selected examples surpris-ingly similar performance despite very different formulations. The most appropriate algorithm selection will then depend on efficiency and ease of implementation for the class of problems considered, i.e. eigenvalue problems, frequency-domain or time-domain. When compared to various finite-element (FE) imple-mentations for the presented numerical examples, the meshless methods appear more accurate and efficient than the FE methods. Those results combined with the convenience of node distribu-tion adaptation makes meshless algorithms very promising for electromagnetic simulations. Index Terms—eigenvalues and eigenfunctions, meshless meth-ods, finite difference methods, radial basis functions. I