Staircase-free finite-difference time-domain formulation for general materials in complex geometries

Abstract

A stable Cartesian grid staircase-free finite-difference time-domain formulation for arbitrary material distributions in general geometries is introduced. It is shown that the method exhibits higher accuracy than the classical Yee scheme for complex geometries since the computational representation of physical structures is not of a staircased nature. Furthermore, electromagnetic boundary conditions are correctly enforced. The method significantly reduces simulation times as fewer points per wavelength are needed to accurately resolve the wave and the geometry. Both perfect electric conductors and dielectric structures have been investigated. Numerical results are presented and discussed.Index Terms-Computational models in electromagnetics and optics, finite-difference time-domain methods, numerical solution of partial differential equations, staircase, time-domain solution of Maxwell's equations.

Second Order Finite Volume Scheme on Tetrahedral Meshes for Three-Dimensional Maxwell’s Equations with Discontinuous Dielectric Permittivity

“…02030-p. 3 continuous variables before averaging. Limited gradients are calculated from averaged values at vertices, values at vertices showing dielectric permittivity discontinuity need to be transformed back from continuous variables.…”

“…This resulted in better accuracy, but not the second order of convergence yet. In [3] an algorithm was suggested that allowed to preserve the second order of approximation. For FVTD the use of continuous variables for linear discontinuities in two dimensions was suggested in [4] and extended to three dimensions and curvilinear discontinuities in [5].…”

A Monte-Carlo MPSTD Analysis of Scattering From Cylinders Buried Below a Random Periodic Rough Surface

“…However, this method has major drawbacks. As pointed out in [12,13], the FDTD approach based on the classical Yee scheme with quadratic cell mapping in space gives the modeled structures a "staircase nature" and requires a number of grids per wavelength. Numerous numerical examples reported in the literature have verified that a fine discretization of 10-20 cells per minimum wavelength is required to obtain acceptable accuracy of solutions.…”

An explicit weighted essentially nonoscillatory time-domain algorithm for 3-D EMC applications with arbitrary media interfaces

“…Due to their substantial complexity and continually varying electrical size [2]- [4] these structures usually involve demanding material interfaces with opposing constitutive parameters which trigger detrimental dispersion errors and late-time oscillatory wave interactions. Scrutinizing the technique's discretization rationale [5]- [10] and the cumulative nature of the prior shortcomings, it becomes evident that a more consistent stencil mechanism should be pursued. To this endeavour, the class of weighted essentially nonoscillatory (WENO) schemes [11]- [14] can proffer potential assistance.…”