Efficient 2-D Finite-Element Solution of Vector Wave Equation in a Class of Curved Polygons

Abstract

We propose an efficient finite-element analysis of the vector wave equation in a class of relatively general curved polygons. The proposed method is suitable for an accurate and efficient calculation of the propagation constants of waveguides filled with pieces of homogeneous materials. To apply the method, we first decompose the 2-D problem domain into a set of curved polygons of a specific characteristic. Then, we divide every polygon into a set of triangular elements with two straight edges. Finally, we introduce a set of hierarchical mixed-order curl-conforming vector basis functions inside every triangular element to discretize the vector wave equation. The advantages of the method are as follows. The curved boundaries of the elements are modeled exactly, and hence, there is no approximation in the geometrical modeling. The 2-D integrals of the matrix elements are reduced to 1-D integrals. Therefore, the matrix filling can be performed very fast. The total number of elements due to the discretization of a given domain is very small, and hence, the discretization of the problem domain takes up a very small percentage of the total computational time. We validate the method by comparing the results with those of the Ansoft High Frequency Structure Simulator simulator and investigate the accuracy and efficiency of the method through a numerical example.