Analysis of Inhomogeneous Rectangular Cavities Using the Variational Meshless Method

The variational meshless method (VMM) has been proposed and demonstrated as a very effective tool for the analysis of 2D structures. In this work, the VMM is extended to 3D eigenvalue problems. In particular, the calculation of the eigenmodes of a rectangular cavity filled with inhomogeneous dielectric material is addressed. The theory is outlined, and the method is validated through the analysis of three different structures. The results are compared with analytical values, when available, and by comparison with a commercial software based on the finite element method. In all cases a good accuracy is obtained for a large number of modes using a limited number of unknowns. Finally, the method proved to be spurious-free.