A stretched coordinate technique for numerical absorption of evanescent and propagating waves in planar waveguiding structures

Gribbons, M.; Pinello, A.P.; Cangellaris, A.C.

doi:10.1109/22.475650

Cited by 9 publications

(3 citation statements)

References 5 publications

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“…The two major problems in the original PML are that it does not absorb evanescent waves efficiently [Berenger, 1999], requiring PML to be placed further away from the scatterer, and also that it suffers from long time instability for some systems [Berenger, 1996]. The first issue has been addressed in [Gribbons et al, 1995] by introducing a stretched coordinates system while the second one was solved in [Kuzuoglu & Mittra, 1996] by increasing the causal nature of PML. These two changes make the most efficient PML formulation in terms of absorption.…”

Section: Introductionmentioning

confidence: 99%

Efficient Abc for the Frequency Dependent Alternating Direction-Implicit FDTD Method

Thiry

Costen

Brown

2007

Int. J. Wireless Opt. Commun.

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Ultra WideBand (UWB) signals have a high potential for a wide range of applications. The Finite-Difference Time-Domain (FDTD) method is widely used in the development of UWB technology but has still two main limitations. One is that material parameters are constant over the whole frequency range. Frequency dependent materials can be accommodated by adopting a Debye model. The other is that the minimum simulation time is bound by the Courant-Friedrichs-Lewy (CFL) condition, which can be solved by the application of the Alternating Direction-Implicit (ADI) scheme. The combination of Debye model and ADI scheme in FDTD results in the Frequency-Dependent (FD) ADI-FDTD method. This paper proposes an adaptation of the most effective Absorbing Boundary Condition (ABC), the Complex Frequency-Shift (CFS) Perfectly Matched Layer (PML), to FD-ADI-FDTD. The formulation of CFS-PML for FD-ADI-FDTD is proposed and its performance is assessed. The influence of the Courant Number (CFLN), the media parameters and the number of layers are investigated. CFS-PML is tightly integrated into the computation update, so that FD-ADI-FDTD must be rewritten to take it into account. With E the electric field, H the magnetic field, D the electric flux density, the permittivity, µ the permeability and ρ the charge density, Maxwell's equations are written as:

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Section: Introductionmentioning

confidence: 99%

Efficient Abc for the Frequency Dependent Alternating Direction-Implicit FDTD Method

Thiry

Costen

Brown

2007

Int. J. Wireless Opt. Commun.

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“…k + 1) + f2kEx+ (ij-k) + f3kEx (i-J k -1) = f4k (7) with Jik! i = 1 3 composed of the Debye parameters and f4k a linear combination of the Debye parameters, the field components Hn, Hn, Dx, Dx 2, Ex, E; , E'n and the recursive functions 1,h n 4,'Z f .…”

Section: Inclusion Of Debye Mediamentioning

confidence: 99%

“…As exposed in [6], the oiginal PML does not absorb evanescent waves efficiently, so the PML has to be placed furhr away from the scantrs for the waves to have enough time to decay. This problem has been taken care of by Gribbons et aL [7] by intrucing a stretched coordinates system inside the PML media so that evannt waves spend enough time in the PML to get absorbed. Another shortcoming of the original PML is tht when simulations involve long grids or signals with long tme signature, which means that the simulation is run long after the initial excitation decayed, late time refiections can show up [8].…”

mentioning

confidence: 99%

Efficient absorbing boundary condition for UWB simulation in frequency dependent ADI-FDTD

Thiry

Costen

2005 IEEE Antennas and Propagation Society International Symposium

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fIhe FmiteDifference Tie-,Domain (FDTD) method has become intng for electromagnetic simulations since the wide availability ofcomputerresource. Its key feaures are its simplicity both in le tn and in the simulation Space. One of its teetdhng problems, togh, is that h e needs to be terminated. Ihis is not an issue when the mulation space is sonded by physical boundaries, like in a cavity, butproblems ariseforfree space simulaion. Thatiswhere Absrbing Boundary Conditions (ABCs) come into play; They aim at absolbng the outgoing wave as if it was still travelling outward. Dffeent echniques to absorb the outgoing wave have been devised. Mur used Maxwell-Gauss' equations to cancel the outgoing wave, reslang in Mur's ABC [1]. It is easy to implement and is c uonaly efficient although it only absorbs accurately orthogonal waves, so comers are a problem and tus it cannot be plaed close to the scaterers Anodter cniqle alled liao's ABC [2] comes fiom wave tery. It only uses wave tieorytoabsorb the outgoing wave and altmugh itis more compl than afirt order Mur's ABC and is also only efficient at absorbing orthogonal waves, another formulation makes use of a damping parameter which can absorb non-orthogonal incident waves [3,41. The last technique, which has received a lot of attention, consists in surrounding the computation space by an artificial anisotpic media. It wes first intrxduced by Brenger and it is called the Perfecdy Matched Layer (PML) ABC [5]. It is th most veatile of the ABCs, effectively absorbing any outgoing waves, from any direction and any fiequency. Because PML emulates a media, it increases the size of the conputatidl space by the size of the absorbing media and moreover the PML media is updated like the computational space and requies some computation. That makes the PML ABC the most memory and computatonally de g ABC.The oiginal PML as proposed by Bdrenger had some problems. The first one was dtat the PML media paamets proposed were not general enough to fit some simulations. As exposed in [6], the oiginal PML does not absorb evanescent waves efficiently, so the PML has to be placed furhr away from the scantrs for the waves to have enough time to decay. This problem has been taken care of by Gribbons et aL [7] by intrucing a stretched coordinates system inside the PML media so that evannt waves spend enough time in the PML to get absorbed. Another shortcoming of the original PML is tht when simulations involve long grids or signals with long tme signature, which means that the simulation is run long after the initial excitation decayed, late time refiections can show up [8]. This is due to the weak causal nature of the original PML fulaon. Kuzuoglu et al. [9] increased the causal naure of the scheme by shifing the frequency dependent pole of the PML media parameters off the real axis into the negative-imaginary half of the complex plane. This is the most general PML formulation, as all the othr can be expressed as special cases of this one. The problem in this approach is that it requires three auxilia...

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Material independent PML absorbers for arbitrary anisotropic dielectric media

Zhao¹,

Juntunen²,

Räisänen³

1997

Electron. Lett.

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A stretched coordinate technique for numerical absorption of evanescent and propagating waves in planar waveguiding structures

Cited by 9 publications

References 5 publications

Efficient Abc for the Frequency Dependent Alternating Direction-Implicit FDTD Method

Efficient Abc for the Frequency Dependent Alternating Direction-Implicit FDTD Method

Efficient absorbing boundary condition for UWB simulation in frequency dependent ADI-FDTD

Material independent PML absorbers for arbitrary anisotropic dielectric media

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