A Lagrangian Approach for the Handling of Curved Boundaries in the Finite-Difference Time-Domain Method

A general methodology for introducing structured nonorthogonal grids into high-order finite-difference time-domain methods

“…p = 3 vs. p = 1) leads to a scheme with lower numerical dispersion and faster convergence. This demonstrates the importance of extending the work in [6], [7] to a high-order framework.…”

“…Moreover, when compared to the high-order scheme in [5], the proposed approach halves the required number of field unknowns per grid cell by retaining the staggering arrangement proposed by Yee [4]. Notice that the proposals in [5]- [7] are based on earlier ideas put forward in [8], [9], and that the present work complements [10], [11], which applies to structured orthogonal grids only.…”

“…The order of accuracy of the employed finite differences is 2L. Lastly, observe that, with a few minor differences, p = 1 corresponds to the second order accurate finite differencing schemes presented in [6], [7].…”

“…For this reason, rather than focusing on different techniques for generating coordinate transformations, the upcoming discussion concentrates on the remaining elements of the proposed nonorthogonal gridding methodology: providing a formulation of Maxwell's equations in a general curvilinear coordinate system that is suited for a FDTD discretization (Section II); and illustrating how the introduction of high-order finite differences enables the use of coarse discretization grids (Section III). While the idea of using coordinate transformations to introduce nonorthogonal structured grids was proposed earlier in [6], [7], this is the first time that it is applied to a high-order scheme. Moreover, when compared to the high-order scheme in [5], the proposed approach halves the required number of field unknowns per grid cell by retaining the staggering arrangement proposed by Yee [4].…”

An efficient methodology for the modeling of electromagnetic wave phenomena in domains with moving boundaries

“…A methodology to alleviate this computational complexity is proposed in this paper. The proposed methodology makes use of the ideas presented in [9], [10] to re-cast the electromagnetic boundary value problem of interest into an equivalent one over a fixed domain with time-invariant boundaries and timevarying electromagnetic properties of the media. Thus, a time-invariant mesh can be used for the discretization of the domain, while the effect of the motion of the boundary is captured through the temporal variation of the electric permittivity and the magnetic permeability of the medium inside the fixed domain.…”