Analysis and Design of Millimeter-Wave Devices with Sharp Edges by an Exponential Spectral-Element-Method

Either weak or strong singularities of the electromagnetic field frequently occur in millimeter-wave devices, because of the presence of sharp edges. The corner branch-points dominate the asymptotic behavior of the basis function coefficients series, thus the convergence is algebraic regardless to the polynomial order of the functions used. In this paper, a Spectral Element Method is presented, which guarantees an exponential rate of convergence also in presence of multiple sharp edges. The method arises from the combination of weighted Chebyshev polynomials and the singular values decomposition. The algorithm is applied to the solution of the Helmholtz equation, in order to analyze waveguide discontinuity problems via the mode-matching technique. The application of the method to the design of dual-polarization diplexers for satellite telecommunication is finally presented.