A Reflectionless Sponge Layer Absorbing Boundary Condition for the Solution of Maxwell's Equations with High-Order Staggered Finite Difference Schemes

Petropoulos, Peter G.; Zhao, Lanhao; Cangellaris, A.C.

doi:10.1006/jcph.1997.5855

Cited by 80 publications

(44 citation statements)

References 26 publications

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“…• In [11], the authors showed that this system (not exactly this one but the one corresponding to the (TM) mode) could be reinterpreted as a zero order perturbation of the usual Maxwell's system, which is strongly well-posed. The general theory [9] permits to conclude that (51) remains strongly well-posed.…”

Section: Remark 21mentioning

confidence: 99%

On the analysis of Bérenger's Perfectly Matched Layers for Maxwell's equations

Bécache¹,

Joly²

2002

ESAIM: M2AN

100

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Abstract.In this work, we investigate the Perfectly Matched Layers (PML) introduced by Bérenger [3] for designing efficient numerical absorbing layers in electromagnetism. We make a mathematical analysis of this model, first via a modal analysis with standard Fourier techniques, then via energy techniques. We obtain uniform in time stability results (that make precise some results known in the literature) and state some energy decay results that illustrate the absorbing properties of the model. This last technique allows us to prove the stability of the Yee's scheme for discretizing PML's.Résumé. Dans ce travail, nous considérons le modèle de couches parfaitement adaptées, dit PML (Perfectly Matched Layers), introduit par Bérenger [3] pour la modélisation de frontières absorbantes enélectromagnétisme. Nous menons une analyse mathématique de ce modèle, d'une part par une analyse modale par transformation de Fourier, d'autre part par des techniquesénergétiques. Nous obtenons ainsi des résultats de stabilité uniforme en temps (qui précisent des résultats déjà connus dans la littérature) etétablissons des résultats de décroissance d'énergie qui illustrent les propriétés d'absorption du modèle. Cette dernière technique permet aussi de démontrer la stabilité du schéma de Yee pour discrétiser les couches absorbantes. Mathematics Subject Classification.

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Section: Remark 21mentioning

confidence: 99%

On the analysis of Bérenger's Perfectly Matched Layers for Maxwell's equations

Bécache¹,

Joly²

2002

ESAIM: M2AN

100

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“…This type of mathematical questions has already been widely investigated by several authors [6,27,29,30,38] in the case of MaxwellÕs equations. For elastodynamics equations, it is easy to show that the PML model is well-posed (cf.…”

Section: Introductionmentioning

confidence: 99%

Stability of perfectly matched layers, group velocities and anisotropic waves

Bécache

Fauqueux

Joly

2003

Journal of Computational Physics

306

355

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Perfectly matched layers (PML) are a recent technique for simulating the absorption of waves in open domains. They have been introduced for electromagnetic waves and extended, since then, to other models of wave propagation, including waves in elastic anisotropic media. In this last case, some numerical experiments have shown that the PMLs are not always stable. In this paper, we investigate this question from a theoretical point of view. In the first part, we derive a necessary condition for the stability of the PML model for a general hyperbolic system. This condition can be interpreted in terms of geometrical properties of the slowness diagrams and used for explaining instabilities observed with elastic waves but also with other propagation models (anisotropic MaxwellÕs equations, linearized Euler equations). In the second part, we specialize our analysis to orthotropic elastic waves and obtain separately a necessary stability condition and a sufficient stability condition that can be expressed in terms of inequalities on the elasticity coefficients of the model.

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“…For the examined problem, a = 12 mm and ε r = 2.2, so (f r ) 110 = 4.94 GHz, which is very close to the first null of Figure 7. In all simulations the computational domain was truncated with an eight-cell sponge layer (Petropoulos et al, 1998) indicating its effectiveness as an ABC for higher order FDTD lattices modeling lossy media.…”

Section: Numerical Resultsmentioning

confidence: 99%

FDTD Algorithm for Microstrip Antennas with Lossy Substrates Using Higher Order Schemes

Prokopidis¹,

Tsiboukis

2004

Electromagnetics

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Higher order spatial schemes are applied to approximate the derivatives of the conducting Maxwell's equations and an analytical study regarding the stability properties and the numerical dispersion of the N-order-in-space and second-order-in-time technique is considered. The hard-to-model effect of dielectric losses on microstrip antennas is investigated and their performance is demonstrated using a fourth-orderin-space and second-order-in-time, finite-difference time-domain scheme in threedimensional calculations.

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A Reflectionless Sponge Layer Absorbing Boundary Condition for the Solution of Maxwell's Equations with High-Order Staggered Finite Difference Schemes

Cited by 80 publications

References 26 publications

On the analysis of Bérenger's Perfectly Matched Layers for Maxwell's equations

On the analysis of Bérenger's Perfectly Matched Layers for Maxwell's equations

Stability of perfectly matched layers, group velocities and anisotropic waves

FDTD Algorithm for Microstrip Antennas with Lossy Substrates Using Higher Order Schemes

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