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

TL;DR

This paper introduces a novel finite-element method for electromagnetic waveguide analysis that accurately models curved boundaries, reduces computational complexity, and efficiently computes propagation constants in complex geometries.

Contribution

It presents a Jacobian separable 2-D finite-element approach with hierarchical curl-conforming basis functions for precise and fast waveguide simulations in curved polygon domains.

Findings

Exact modeling of curved boundaries improves accuracy.

Reduction of 2-D integrals to 1-D accelerates computations.

Small element count enhances efficiency and speed.

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. 2-D integrals of the matrix elements are reduced to 1-D integrals. Therefore, the matrix filling can be performed very fast. 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 Ansoft HFSS simulator and investigate the accuracy and efficiency of the method through some numerical examples.