Finite-Element Time-Domain Analysis of Electrically and Magnetically Dispersive Periodic Structures

Riley, D.J.; Jin, Jian‐Ming

doi:10.1109/tap.2008.2005454

Cited by 28 publications

(19 citation statements)

References 14 publications

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“…The final result can be stated as

\frac{\tilde{k} - k}{k} \approx \frac{1}{12} ω^{2} Δ t^{2} + \frac{1}{8} χ_{m} (ω) ω^{2} Δ t^{2} + \frac{1}{24} \frac{χ_{m} (ω)}{1 + χ_{m} (ω)} {(j ω + b_{m})}^{2} Δ t^{2}

where the first term is the temporal discretization error of the standard FETD, and the remaining terms represent the error induced by the modeling of the magnetic dispersion. Compared with , it is observed that there is an extra error term

\frac{1}{8} χ_{m} (ω) ω^{2} Δ t^{2}

; therefore, the conclusion is that the magnetic dispersion modeling in this paper is slightly more accurate than that in .…”

Section: Error Analysismentioning

confidence: 76%

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Modeling of doubly lossy and dispersive media with the time‐domain finite‐element dual‐field domain‐decomposition algorithm

Jin

2012

Int J Numerical Modelling

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SUMMARY A numerical scheme is presented for the time‐domain finite‐element modeling of an electrically and magnetically lossy and dispersive medium in the dual‐field domain‐decomposition method. Existing approaches for modeling doubly lossy and dispersive media are extended to the dual‐field case, yielding a general dual‐field domain‐decomposition scheme for modeling large‐scale electromagnetic problems involving such media. A quantitative analysis is performed to estimate the error induced by the modeling of medium dispersion. Copyright © 2012 John Wiley & Sons, Ltd.

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“…The final result can be stated as

\frac{\tilde{k} - k}{k} \approx \frac{1}{12} ω^{2} Δ t^{2} + \frac{1}{8} χ_{m} (ω) ω^{2} Δ t^{2} + \frac{1}{24} \frac{χ_{m} (ω)}{1 + χ_{m} (ω)} {(j ω + b_{m})}^{2} Δ t^{2}

\frac{1}{8} χ_{m} (ω) ω^{2} Δ t^{2}

; therefore, the conclusion is that the magnetic dispersion modeling in this paper is slightly more accurate than that in .…”

Section: Error Analysismentioning

confidence: 76%

“…e Àb e mΔt : : e j nÀmÀ1 (27) and it can be updated using the recursive convolution algorithm [2,[5][6][7][8]:…”

Section: Computation Of Convolutions and Construction Of Matrix Equatmentioning

confidence: 99%

Modeling of doubly lossy and dispersive media with the time‐domain finite‐element dual‐field domain‐decomposition algorithm

Jin

2012

Int J Numerical Modelling

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“…There are a lot of available mathematical and numerical results, especially for the timeharmonic wave equations [8,11,16,26,[28][29][30]33,39,40,43]. The time-domain problems have received considerable attention due to their capability of capturing wide-band signals and modeling more general material and nonlinearity [4,38,42]. Many approaches are attempted to solve numerically the time-domain problems such as coupling of boundary element and finite element with different time quadratures [12,14,18,27,34,40].…”

Section: Introductionmentioning

confidence: 99%

Analysis of transient acoustic scattering by an elastic obstacle

Zhang

2019

Communications in Mathematical Sciences

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Consider the scattering of an acoustic plane wave by a bounded elastic obstacle which is immersed in an open space filled with a homogeneous medium. This paper concerns the mathematical analysis of the coupled two-and three-dimensional acoustic-elastic wave propagation problem in the time-domain. A compressed coordinate transformation is proposed to reduce equivalently the scattering problem into an initial-boundary value problem in a bounded domain over a finite time interval. The reduced problem is shown to have a unique weak solution by using the Galerkin method. The stability estimate and an a priori estimate with explicit time dependence are obtained for the weak solution. The reduced model problem is suitable for numerical simulations. The proposed method is applicable to many other time-domain scattering problems imposed in open domains.2010 Mathematics Subject Classification. 78A46, 65C30. Key words and phrases. Time domain, acoustic wave equation, elastic wave equation, fluid-structure interaction, well-posedness and stability, a priori estimate.

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“…The time-domain scattering problems have recently attracted considerable attention due to their capability of capturing wide-band signals and modeling more general material and nonlinearity [5,12,14,20,26], which motivates us to tune our focus from seeking the best possible conditions for those physical parameters to the time-domain problem. Comparing with the time-harmonic problems, the time-domain problems are less studied due to the additional challenge of the temporal dependence.…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic scattering for time-domain Maxwell’s equations in an unbounded structure

Gao

2017

Math. Models Methods Appl. Sci.

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The goal of this work is to study the electromagnetic scattering problem of time-domain Maxwell's equations in an unbounded structure. An exact transparent boundary condition is developed to reformulate the scattering problem into an initial-boundary value problem in an infinite rectangular slab. The well-posedness and stability are established for the reduced problem. Our proof is based on the method of energy, the Lax-Milgram lemma, and the inversion theorem of the Laplace transform. Moreover, a priori estimates with explicit dependence on the time are achieved for the electric field by directly studying the time-domain Maxwell equations.

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Finite-Element Time-Domain Analysis of Electrically and Magnetically Dispersive Periodic Structures

Cited by 28 publications

References 14 publications

Modeling of doubly lossy and dispersive media with the time‐domain finite‐element dual‐field domain‐decomposition algorithm

Modeling of doubly lossy and dispersive media with the time‐domain finite‐element dual‐field domain‐decomposition algorithm

Analysis of transient acoustic scattering by an elastic obstacle

Electromagnetic scattering for time-domain Maxwell’s equations in an unbounded structure

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