Application of Multi-Domain GDQ Method to Analysis of Waveguides with Rectangular Boundaries

Determination of the TE and TM modes in arbitrarily shaped waveguides using a hypersingular boundary element formulation

“…The results were computed with 28, 56 and 112 elements, and compared with those from Ref. [6] with 50 elements for the TM case and 40 for the TE and [9], showing again very good accordance. The last example, that of a T-septate rectangular waveguide of dimensions a = 1.0 cm, b =0.45 cm, d =0.25 cm, W =0.125 cm, is the most demanding one ( Table 7).…”

“…A surface integral formulation [6,7] or an element free method [8] like the FEM has to take into account internal points while a boundary element formulation takes into account only points in the boundary, which requires less computational effort when treating open-boundary problems or problems with lossy conductors, although FEM could be faster when there are many dielectric interfaces. Other formulations like the generalized differential quadrature [9] are also more computationally efficient but need to use multi-domain approaches which need to add unknowns inside the problem domain. In this work the hypersingular boundary element is used for the first time thus allowing for the analysis of problems exhibiting singularities such as the ones occurring in domains with cracks, which can not be analyzed with an usual BEM formulation as in Ref.…”

The Methods of External Excitation for Analysis of Arbitrarily-Shaped Hollow Conducting Waveguides

“…In Table 9 we test a convergence of the eigenvalues. The results are compared with the results of Shu and Chew [15] obtained by the global method of generalized differential quadrature (GDQ). Note that the L-shaped domain considered in [15] is smaller than the one depicted in Fig.…”

“…The analysis of waveguides with a complex cross-section is of a great interest for engineering application [13,14]. To handle such problems the generalized differential quadrature method has been developed and applied for waveguide analysis in [15]. Efficient numerical methods for analysis of arbitrary cross sections waveguide problems have been developed recently [16][17][18].…”

Implementation of Fourier Expansion Based Differential Quadrature Method (FDQM) and Polynomial Based Differential Quadrature Method (PDQM) for the 2D Helmholtz Problem

“…Helmholtz equation is the governing equation for many engineering problems such as waveguides in electromagnetic fields, vibration of membranes and water wave diffraction in offshore structure engineering (Shu and Chew, 1999). In addition, acoustic waves and microwaves can be simulated by the Helmholtz equation.…”