SUMMARY Based on the same concept as generalized diAerential quadrature (GDQ), the method of Fourier expansionbased diAerential quadrature (FDQ) was developed and then applied to solve the Helmholtz eigenvalue problems with periodic and non-periodic boundary conditions. In FDQ, the solution of a partial diAerential equation is approximated by a Fourier series expansion. The details of the FDQ method and its implementation to sample problems are shown in this paper. It was found that the FDQ results are very accurate for the Helmholtz eigenvalue problems even though very few grid points are used. #1997 John Wiley & Sons, Ltd.

Fourier expansion‐based differential quadrature and its application to Helmholtz eigenvalue problems

A procedure is described for obtaining the cutoff wave numbers of transverse electric (TE) and transverse magnetic (TM) modes in waveguides of arbitrary cross section. A surface integral equation approach is used in which the E-field equation has been transformed into a matrix equation using the method of moments. An iterative technique is used to pick the eigenvalues of the solution matrix which corresponds to the waveguide cutoff wave numbers. The salient features of this technique are its speed, its simplicity, and the absence of any spurious modes when waveguides of arbitrary cross section are treated. The first four modes are tabulated for various waveguides, and the results are in very good agreement with published data. >

Computation of cutoff wavenumbers of TE and TM modes in waveguides of arbitrary cross sections using a surface integral formulation

A numerical procedure based on the finite-difference method and simultaneous iteration of the power method in conjunction with the Chebyshev acceleration technique is utilized to analyze the metallic waveguides. Due to the efficiency of the present sparse matrix eigenproblem solver, lots of unknowns can be used in the domains of the waveguide cross-sections. Therefore, accurate cutoff wavenumbers or frequencies can be obtained by using the simple finite-difference method for the commonly used metallic waveguides such as the L-shaped, single-ridged, double-ridged, and rectangular coaxial waveguides. Some discrepancies with the numerical results in the recent literature are found and detailed discussions are provided to verify the correctness of the present results. >

Analysis of metallic waveguides with rectangular boundaries by using the finite-difference method and the simultaneous iteration with the Chebyshev acceleration

A procedure for determining the cutoff wavenumbers of partially dielectric filled waveguides of arbitrary cross section is presented. A number approach based on surface integral formulations and the method of moments is used to obtain a matrix equation. Muller's method is then applied to find the wavenumbers that make the matrix determinant vanish. These are the cutoff wavenumbers. On the conducting walls of the waveguide, perfect electric conductor, perfect magnetic conductor, and imperfect conductor surfaces are considered. The transverse electric and magnetic cases are treated separately. The impedance boundary condition and the symmetry of the waveguide cross section are used to reduce the matrix size in the method of moments. Spurious modes have not been observed using this method. To validate its accuracy, results for circular, partially filled rectangular, and two-walled corrugated rectangular waveguides are compared to analytical results. Examples such as T-septate rectangular, coaxial, and dielectric-loaded double-ridged waveguide are also considered. >

Computation of cutoff wavenumbers for partially filled waveguide of arbitrary cross section using surface integral formulations and the method of moments

By using the polynomial approximation and superquadric functions in the Rayleigh-Ritz procedure, a unified method has been proposed to analyze conducting hollow waveguides of a large class of cross sections in our previous paper. Some useful and complicated cross-sectional waveguides in the microwave system, namely, eccentric annular, pentagonal, L-shaped, single-ridged, and double-ridged waveguides are analyzed in this paper. Compared with other numerical methods, this method has the advantages of being straightforward, accurate, and computational effective.

Analysis of metallic waveguides of a large class of cross sections using polynomial approximation and superquadric functions

This paper describes the use of the conjugate gradient method in conjunction with the finite difference method for the calculation of the propagation characteristics of TE and TM modes, including cutoff wavenumbers and field distribution, of hollow conducting waveguides of arbitrary cross sections. This method is quite fast and accurate and can be applied in a straightforward fashion for the analysis of both TE and TM modes in waveguides of arbitrary cross sections. In order to check the accuracy of this method, the new approach has been applied to compute the cutoff wavelength of a rectangular waveguide as analytical results are available for this problem. This method has also been applied to compute the first six TE and TM modes for L-shaped, single ridge, vaned rectangular, T-septate and rectangular coaxial waveguides. Comparison of accuracy is made whenever data is available. Since the conjugate gradient method is an iterative method, computer storage is 6N instead of N2 for conventional matrix method...

Kamal Athar

Papers

Computation of the propagation characteristics of TE and TM modes in arbitrarily shaped hollow waveguides utilizing the conjugate gradient method