A Spectral-Element Method for the Analysis of 2-D Waveguide Devices With Sharp Edges and Irregular Shapes

This paper presents an efficient implementation of spectral-element methods (SEMs) for the analysis of 2-D wave-guide components with sharp edges. The well-known problem of ill conditioning of the mass matrix when very high-order polynomial basis functions are augmented with singular functions is addressed. A numerical process for the definition of a set of orthonormal entire-domain boundary-adapted functions incorporating the relevant edge conditions is presented. These functions are synthesized by applying the singular value decomposition algorithm to different sets of weighted Chebyshev polynomials. The application of the method to the analysis of both E- and H-plane components with sharp edges and irregular shapes is reported. Comparisons with various numerical methods and with experimental data show that the exponential convergence, typical of SEMs, is achieved.