Analysis of Curved Boundaries by FDTD and FE Methods

Curved waveguide surfaces have been dealt with by using modified finite difference time domain (FDTD), finite element method (FEM) and hybrid methods. The propagation characteristics and S-parameters of the circular waveguides have been determined, and results compared with the analytic results, thus determining the computational efficiency of each of the method. Both FDTD and FE techniques are extensively used in the analysis and design of microwave problems. For the analysis of curved boundary, however, the traditional FDTD method suffers from significant degradation in accuracy due to staircasing approximation. A novel approach is presented here which combines the efficiency of the Cartesian mesh with the accuracy of the conformal grid. Further, an efficient finite element method is presented in which a variational expression is formulated in terms of transverse electric and magnetic field components. The method can be applied to anisotropic media also. Finally a partially prism gridded FDTD method is proposed which hybridizes the prism based FEM to handle the curved boundaries and rectangular gridded FDTD for most of the regular region.