A hybrid FDTD-wavelet-Galerkin technique for the numerical analysis of field singularities inside waveguides

Dispersion characteristic and stability analysis for an arbitrary MRTD scheme with variable mesh

“…On the other hand, one can employ large cells for areas with smooth field variations and in which MRTD scheme can be applied to compute the spatial derivatives by using the structured mesh proposed by Monk 11. Therefore, in the volume we have a combination of MRTD‐FDTD schemes by each dimension according to the size of the cell in a similar way proposed by Kosmanis 10 but with variable meshing. Advantages of variable meshing reduce substantially the execution time (six times faster) for the same accuracy as will be shown further.…”

“…Coupling with FDTD was developed with Haar family 8, 9. For instance, a hybrid method developed by Kosmanis 10 shows good agreement in the treatment of singularities. It is rather proposed in this paper a FDTD computation for regions with strong field variations only as it exhibits some similar dispersion when compared with MRTD case.…”

A nonorthogonal higher-order wavelet-oriented FDTD technique for 3-D waveguide structures on generalized curvilinear grids

“…The novel algorithm also allows accurate treatment of field singularities, such as conductive wedges, since it embodies the spatially-localized FDTD-Wavelet-Galerkin technique [9]. According to the latter, the computational domain is divided into regions of sharp (in the vicinity of the discontinuities) and regions of smooth field transitions (rest of the domain).…”

“…In (17), are coefficients that depend only on the scaling function selected [9]. On the contrary, the rest of the computational domain, where singularities are absent, is treated by the more convenient, linear FDTD method.…”

“…For a precise and consistent simulation of the continuous physical space in terms of its discretized counterpart, the difference operators in (2) are expressed by the following forms which completely exploits the geometry of the elementary cell, as shown in According to the nonstandard regime, temporal discretization receives the subsequent form (9) where denotes third-order time differentiation and is the respective correction function. Time integration (except of the leapfrog scheme) is performed by means of the fourth-stage Runge-Kutta integrator, generally given by (10) in which is the spatial discretization matrix and the order of the integrator.…”