Time‐domain finite‐element modeling of electrically and magnetically dispersive medium via recursive FFT

Li, Xiaolei; Jin, Jian‐Ming

doi:10.1002/mop.23488

Cited by 6 publications

(5 citation statements)

References 5 publications

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“…(13) with the recursive FFT algorithm, we need to divide Eq. (13) into summations of lengths of 2 p (except the last one) starting with N the biggest possible 2 p , and in an descending order [11] …”

Section: Recursive Fast Fourier Transformmentioning

confidence: 99%

Wideband Finite-Difference Time-Domain Modeling of Graphene via Recursive Fast Fourier Transform

Afshar¹,

Akbarzadeh-Sharbaf²,

Giannacopoulos³

et al. 2017

PIER C

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Abstract-An efficient method based on the recursive fast Fourier transform (FFT) to incorporate both the intra-band and inter-band conductivity terms of graphene into the finite-difference time-domain (FDTD) method is proposed. As it only requires numerical values of the conductivity, it not only does not enforce any restrictions on the conductivity models, but also can directly take into account material properties obtained from measurement. It reduces the total computational cost from O(N 2 ) to O(N log 2 N ) where N is the length of the unknown. The FDTD method is also modified and proven to retain the stability condition of the standard FDTD method.

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Section: Recursive Fast Fourier Transformmentioning

confidence: 99%

Wideband Finite-Difference Time-Domain Modeling of Graphene via Recursive Fast Fourier Transform

Afshar¹,

Akbarzadeh-Sharbaf²,

Giannacopoulos³

et al. 2017

PIER C

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“…Now, we map the latter one onto the -domain using Möbius transformation [11]. The appropriate Möbius transformation consistent with the CN method (9) can be easily obtained using -transform as (18) substituting (18) into (15) results in the following permittivity in the -domain (19) where the coefficients and are related to and ( , and ). Using , the difference form of can be reached simply.…”

Section: A Update Equation For Electric Field Constitutive Relationmentioning

confidence: 99%

“…Unfortunately, just a few papers are dedicated to the FETD formulation in such media [17]- [19]. To the best knowledge of authors, all FETD solutions of the vector wave equation for general electromagnetic problems in dispersive media rely on convolution-based approaches.…”

Section: Introductionmentioning

confidence: 99%

“…These methods not only can't model arbitrary frequency-dependent materials, but also become cumbersome for materials described with multiple poles. Although the first problem has been alleviated using recursive fast Fourier transform (FFT) [19], the computation cost of the recursive FFT is added to the simulation. In contrast to the finite-element (FE) formulation for the vector wave equation, dispersion of the media can be easily incorporated in the mixed FETD formulations, because constitutive relations can be derived separately.…”

Section: Introductionmentioning

confidence: 99%

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Finite-Element Time-Domain Solution of the Vector Wave Equation in Doubly Dispersive Media Using Möbius Transformation Technique

Akbarzadeh-Sharbaf

Giannacopoulos

2013

IEEE Trans. Antennas Propagat.

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Several finite-element time-domain (FETD) formulations to model inhomogeneous and electrically/magnetically/doubly dispersive materials based on the second-order vector wave equation discretized by the Newmarkscheme are developed. In contrast to the existing formulations, which employ recursive convolution (RC) approaches, we use a Möbius transformation method to derive our new formulations. Hence, the obtained equations are not only simpler in form and easier to derive and implement, but also do not suffer from the intrinsic limitations of the RC methods in modeling arbitrary high-order media. To obtain the formulations, we first demonstrate that the update equation for the electric field strength in the mixed Crank-Nicolson (CN) FETD formulation, which is based on expanding the electric and magnetic field in terms of the edge and face elements in space and discretizing the resultant first-order differential equations using Crank-Nicolson scheme in time, is equivalent to the unconditionally stable (US) second-order vector wave equation for the same variable ( ) discretized by the Newmarkmethod with . In addition, we show that the update equation for the magnetic flux density in CN-FETD is the same as the second-order vector wave equation for on the dual grid discretized again by a similar Newmarkmethod. Subsequently, thanks to the mixed FETD formulation properties, we derive update equations for the constitutive relations using a Möbius transformation method separately. In addition, we use the shown equivalence to derive formulations based on the vector wave equation. Finally, several numerical examples are solved to validate the developed formulations. Index Terms-Dispersive media, finite-element time-domain method. Ali Akbarzadeh-Sharbaf (S'09) received the M.Sc. degree in electrical engineering from Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran in 2011. He is currently working toward the Ph.D. degree at the Computational Analysis and Design Laboratory (CAD Lab), department of electrical and computer engineering, McGill University. Mr. Akbarzadeh-Sharbaf is a recipient of the Iran Telecommunication Research Center (ITRC) grant to support his M.Sc. thesis. He is also a recipient of the McGill Engineering Doctoral Award (MEDA) and the Eric. L. Adler fellowship in electrical engineering, McGill University. His research interests include computational electromagnetics, especially differential-based techniques. Dennis D. Giannacopoulos ('90-M'92) received the B.Eng.and Ph.D. degrees in electrical engineering

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“…These approaches employed a recursive convolution algorithm to speed up the evaluation of the time convolutions induced by the medium dispersion, where the time‐domain electric and magnetic susceptibility functions are expanded into a sum of exponential functions. A more general approach based on the recursive fast Fourier transform algorithm has also been developed, which does not require the aforementioned expansion of the susceptibility functions . It is useful when the susceptibility functions cannot be accurately expressed using a small number of exponential functions.…”

Section: Introductionmentioning

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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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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Time‐domain finite‐element modeling of electrically and magnetically dispersive medium via recursive FFT

Cited by 6 publications

References 5 publications

Wideband Finite-Difference Time-Domain Modeling of Graphene via Recursive Fast Fourier Transform

Wideband Finite-Difference Time-Domain Modeling of Graphene via Recursive Fast Fourier Transform

Finite-Element Time-Domain Solution of the Vector Wave Equation in Doubly Dispersive Media Using Möbius Transformation Technique

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

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