Pitfalls of staircase meshing

Holland, Robert C.

doi:10.1109/15.247856

Cited by 90 publications

(64 citation statements)

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“…Later Holland [6] published work that considered the scattering from a 2D PEC cylinder, it was determined that accurate results could be achieved using a stair-cased mesh if the mesh size was small enough, however use of a conformal technique could achieve a reduction in run time by an approximate factor of 256 by allowing a coarser mesh. The problem of scattering from curved surfaces was revisited by Häggblad [7] who showed that the large errors were found close to the surface, but the errors observed further from the surface were reduced.…”

Section: Introductionmentioning

confidence: 99%

Errors in the shielding effectiveness of cavities due to stair-cased meshing in FDTD: Application of empirical correction factors

Bourke

Dawson

Flintoft

et al. 2017

2017 International Symposium on Electromagnetic Compatibility - EMC EUROPE

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Section: Introductionmentioning

confidence: 99%

Errors in the shielding effectiveness of cavities due to stair-cased meshing in FDTD: Application of empirical correction factors

Bourke

Dawson

Flintoft

et al. 2017

2017 International Symposium on Electromagnetic Compatibility - EMC EUROPE

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“…This would be due to the inaccuracy of reflections from the stair step approximation of the cylinder, and it seems to be Downloaded 08/11/13 to 114.70. persistent even for finer resolutions. A similar study revealing the inaccuracies for oblique electromagnetic interfaces is done in [9] for Yee's algorithm. Holland [9] suggests a conformal mesh approach as a remedy.…”

Section: Further Grid Refinement Testsmentioning

confidence: 99%

“…A similar study revealing the inaccuracies for oblique electromagnetic interfaces is done in [9] for Yee's algorithm. Holland [9] suggests a conformal mesh approach as a remedy. The persistence of the inaccuracy from the stair step approximation is not too surprising and highlights the need for methods such as the DDM that treat the boundaries accurately.…”

Section: Further Grid Refinement Testsmentioning

confidence: 99%

“…We mimic the circular PEC object (i.e., the cylinder) with rectangular PEC patches (see Figure 8.2(b)) where B y -and D z -fields are specified with zero for the grid points within or on the PEC object. B x -fields are computed using the backward-time forward-space scheme as a numerical boundary condition (a similar PEC implementation for Yee's algorithm can be found in [9]). These results are compared with the case in Figure 8.2(a) where (Δ, N φ ) = (1/20, 48) (see Figure 8.4).…”

Section: Further Grid Refinement Testsmentioning

confidence: 99%

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The Domain Decomposition Method for Maxwell's Equations in Time Domain Simulations with Dispersive Metallic Media

Park¹,

Strikwerda²

2010

SIAM J. Sci. Comput.

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Abstract. The domain decomposition method based on overlapping grids is developed to solve the two-dimensional Maxwell equations in the time domain. The finite difference schemes for rectangular and polar coordinate systems are presented. Since interpolation plays a crucial role in our method, the Newton and the Fourier interpolation methods are surveyed in detail. The computational studies of the electromagnetic wave propagation in free space and the back-scattering by a perfect electric conducting object of a circular shape are performed to test the accuracy, the convergence, and the efficiency of our method. Moreover, we give a methodology to model dispersive media in time domain simulations by introducing Drude conductivity in the constitutive equations. The problem of light scattering by metallic nanoparticles is solved, and its results show that our algorithm is efficient and reliable in capturing the small scale phenomena. Key words.Maxwell's equations, finite difference schemes, computational electromagnetics, domain decomposition methods, interpolation, dispersive media, metallic nanoparticles AMS subject classifications. 65M06, 78M20 DOI. 10.1137/070705374 1. Introduction. One of the main difficulties in the development of reliable tools for computational electromagnetics (CEM) based on conventional algorithms like Yee's method [20,21] (commonly known as the finite difference time domain method (FDTD)) is the treatment of curved interfaces. Brute force discretization using only a rectangular grid requires excessively small grid sizes to reasonably resolve the curvature of the interface, and this frequently forces the use of large amounts of memory and unreasonably long computation times. Furthermore, numerical artifacts (known as staircasing errors) can be introduced and corrupt the solutions. Other algorithms for CEM are discussed in [3,4,7,12,15,20].Recently, domain decomposition methods (DDMs) [18] based on overlapping (or composite) grids have been successfully applied to CEM problems with complex geometries [6,8]. Henshaw [8] solved Maxwell's equations as a second-order vector wave equation rather than as a first-order system and developed high-order schemes by discretizing the Laplace operator. The jump (or transmission) condition at the interface of two different constant media are derived using boundary-(or interface-) fitted grids.In this paper, we suggest a more general method. We solve the two-dimensional Maxwell equations as a first-order system with constitutive equations. By doing this, we separate numerical stability issues from material modeling issues (i.e., stable schemes for Maxwell's equations can be used with various materials by simply

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“…Previously, there has been some analysis of staircasing errors associated with perfectly conducting boundaries. For example, Cangellaris and Wright [7] rigorously analyzed the staircased representation of a planar surface tilted 45 to the grid, while Holland [8] analyzed errors associated with a slightly tilted planar scatterer. However, the analysis in these papers did not give guidelines for avoiding staircasing errors that would hold for general problems in which a staircase approximation is used.…”

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confidence: 99%

FDTD simulations of TEM horns and the implications for staircased representations

Schneider

Shlager

1997

IEEE Trans. Antennas Propagat.

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Abstract-Two-dimensional (2-D) TEM horns are modeled using the finite-difference time-domain (FDTD) method. The boundary walls are perfect electric conductors and one wall, which does not align with the Cartesian grid, is approximated using a staircased representation. By carefully comparing the FDTD results to those of the analytic solution, one can make conclusions about the coarseness with which a boundary can be represented. It is found that staircasing errors are small when the staircase diagonal (the hypotenuse of the right triangle created by the stairstep) is smaller than half a wavelength at the highest significant frequency in the excitation. This rule-of-thumb is put forward as a necessary condition for the discretization of general problems. Results are also provided for some simple FDTD schemes that are designed to reduce staircasing errors. By using large aspect-ratio cells, a grid can be constructed that satisfies the rule-of-thumb given above. While this approach eliminates general staircasing errors, some errors persist owing to the presence of step discontinuities immediately adjacent to the horn feed. These errors can be further reduced by using a cell-splitting approach. It is shown that the contour path FDTD technique can be used to eliminate nearly all staircasing errors, while some additional improvement is shown to be provided by using a stabilized contour path FDTD approach. Finally, a recently proposed conformal technique that permits simple implementation is shown to provide results comparable with those of the stabilized contour path approach.Index Terms-FDTD methods, horn antennas.

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Pitfalls of staircase meshing

Cited by 90 publications

References 13 publications

Errors in the shielding effectiveness of cavities due to stair-cased meshing in FDTD: Application of empirical correction factors

Errors in the shielding effectiveness of cavities due to stair-cased meshing in FDTD: Application of empirical correction factors

The Domain Decomposition Method for Maxwell's Equations in Time Domain Simulations with Dispersive Metallic Media

FDTD simulations of TEM horns and the implications for staircased representations

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