A method for creating twelve-node finite element meshes to find the cutoff wave number for polygonal and circular waveguides

The numerical solution of the Helmholtz equation-driven electromagnetic waveguide eigenvalue issue is presented using the finite element ‎method. This work utilized a 2D automated 12-noded mesh generator, run with Maple 13, to produce a highly efficient, straightforward, and accurate higher-order technique for the current work. A transcendence automated discretization is constructed. Meshes with quadrilateral ‎elements are used for wave-guiding structures that are square, L-shaped, and unit-circular regions, but this explanation of the finite element ‎approach is sufficient for the purposes at hand. In any numerical simulation that uses the finite element approach, meshing procedures are ‎extremely important, the approach is shown for several waveguide configurations, and the results are compared to the most ‎reliable numerical or analytical results. Since there is no curvature loss, the results demonstrate that the proposed methodology is precise and ‎effective for producing finite element models of complex structures, this article provides a cutoff frequency determination using the Maple ‎program and commercial software analysis results are taken into account for the comparison, demonstrating that the computation results for ‎electromagnetic applications, this process can be used to obtain the most efficient energy transmission.