A Simple and Efficient Higher Order Finite Element Scheme for Helmholtz Waveguides

Abstract

This paper presents a simple and efficient finite element scheme for computing the cutoff wave numbers of arbitrary-shaped waveguides using higher order triangular elements. The waveguide geometry is divided into a set of triangular elements and each of these elements is mapped to a standard isosceles triangle by discritizing with subparametric finite elements. For waveguides containing arbitrary cross sections, the transformation is done using a series of higher order parabolic arcs. In this case, the curve boundaries are approximated by curved triangular finite elements and then transformed to an isosceles triangle. Numerical results are illustrated to validate the present approach. The obtained results have converged very well with the existing literature with minimum number of triangular elements, degree of freedoms, order of computational matrix, etc.