Efficient Calculation of the 3-D Rectangular Waveguide Green’s Functions Derivatives by the Ewald Method

In this contribution, the Ewald method has efficiently been applied to accelerate the computation of the rectangular waveguide Green’s functions (GFs) derivatives. Based on previous works, we have outlined new approximation formulae that avoid the evaluation of computationally expensive complementary error functions of complex argument, needed by the Ewald method. This is possible when the internal medium of the rectangular waveguide is homogeneous and lossless. On the other hand, different convergence numerical studies have been carried out, showing a similar convergence rate for computing the original GFs and their derivatives. Moreover, we have checked that the computational time is only slightly increased for obtaining the derivatives as compared to the original GFs, after the application of these new techniques. The newly derived expressions are useful for the evaluation of electromagnetic fields, the characterization of dielectric materials and step discontinuities between rectangular waveguides, and the analysis of rectangular cavities using integral equation formulations. For validation, the electric field produced by a surface electric current density with a rectangular pulse distribution has been evaluated, using the new proposed expressions. These results have been compared to simulations provided by full-wave finite elements commercial software to verify their correctness, exhibiting a good agreement.