Exploiting Symmetries in the Variational Meshless Method for 3-D Inhomogeneous Cavities

The variational meshless method (VMM) is a novel numerical algorithm that combines the intrinsic advantages of the meshless method based on the use of radial basis functions (RBFs) with the reliability of the variational formulation of electromagnetic boundary problems. It has been originally proposed and demonstrated in the analysis of 2-D structures, both homogeneous and inhomogeneous, aiming at the determination of the mode spectrum and the dispersion diagram. In this article, the VMM is extended to the calculation of the resonant modes of 3-D inhomogeneous cavities. The full theory is presented with implementation details. Moreover, the exploitation of symmetries is also discussed, which significantly speedup the method. Some examples are reported, and the results of the VMM are compared against either analytical values (when available) or commercial numerical codes based on the finite element method (FEM). In all cases, the VMM provides a large number of resonant modes with a limited number of unknowns, exhibiting high accuracy in short computing time.