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We propose an efficient finite-element analysis of the vector wave equationin a class of relatively general curved polygons. The proposed method issuitable for an accurate and efficient calculation of the propagation constantsof 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 aspecific characteristic. Then we divide every polygon into a set of triangularelements with two straight edges. Finally, we introduce a set of hierarchicalmixed-order curl-conforming vector basis functions inside every triangularelement to discretize the vector wave equation. The advantages of the methodare as follows. The curved boundaries of the elements are modeled exactly andhence there is no approximation in the geometrical modeling. 2-D integrals ofthe matrix elements are reduced to 1-D integrals. Therefore, the matrix fillingcan be performed very fast. Total number of elements due to the discretizationof a given domain is very small, and hence the discretization of the problemdomain takes up a very small percentage of the total computational time. Wevalidate the method by comparing the results with those of Ansoft HFSSsimulator and investigate the accuracy and efficiency of the method throughsome numerical examples.

A Jacobian Separable 2-D Finite-Element Method for Electromagnetic Waveguide Problems