Application of automated cubic-order mesh generation for efficient energy transfer using parabolic arcs for microwave problems

Abstract This paper aims to offer an efficient, simple and accurate cubic-order subparametric finite element technique utilizing 2-D automated mesh generator for microwave applications. The proposed technique utilizes the best discretization procedure, the finest quadrature rule and an excellent subparametric finite element algorithm for obtaining the numerical solutions of the Helmholtz equation. The high-quality automated mesh generator MATLAB code developed for the present work using HOmesh2d.m and CurvedHOmesh2d.m are provided. This approach utilizes up to cubic-order triangular mesh for arbitrary waveguide structures. The meshes with one side curved cubic-order triangular elements are proposed with parabolic arcs for curved waveguide structures. For regular waveguide structures with sharp edges having singularities, the utilization of unstructured cubic-order triangular meshes with refinement for the technique is proposed. The method is demonstrated for six different waveguide structures and the outcomes obtained are compared with the best available numerical or analytical results. The results show that the proposed technique produces an efficient and most accurate finite element results for the finite element analysis performed for waveguide structures with singularities and curved geometries as there is no curvature loss. Thus, the proposed subparametric finite element technique with the automated mesh generator is verified to yield a viable approach for getting the most precise numerical result for the 2-D Helmholtz equation in distinct waveguide cross-sections. Therefore, this approach can be used to produce the most efficient energy transfer for microwave applications.