Stability and Dispersion Analysis for ADI-FDTD Method in Lossy Media

Fu, Weiming; Tan, Eng Leong

doi:10.1109/tap.2007.893378

Cited by 30 publications

(20 citation statements)

References 17 publications

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“…The averaging scheme [4][5][6] is one of the most common schemes used where the conductivity terms are averaged between two time indices in both substeps. The scheme calls for the following update procedure:…”

Section: Averagingmentioning

confidence: 99%

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Unified Efficient Fundamental Adi-FDTD Schemes for Lossy Media

Heh¹,

Tan²

2011

PIER B

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Abstract-This paper presents the unified efficient fundamental alternating-direction-implicit finite-difference time-domain (ADI-FDTD) schemes for lossy media. The schemes presented include averaging, forward-forward, forward-backward and novel exponential time differencing schemes. Unifications of these schemes in both conventional and efficient fundamental forms of source-incorporated ADI-FDTD are provided. In the latter, they are formulated in the simplest, most concise, most efficient, and most fundamental form of ADI-FDTD. The unified update equations and implementation of the efficient fundamental ADI-FDTD schemes are provided. Such efficient fundamental schemes have substantially less right-hand-side update coefficients and field variables compared to the conventional ADI-FDTD schemes. Thus, they feature higher efficiency with reduced memory indexing and arithmetic operations. Other aspects such as field and parameter memory arrays, perfect electric conductor and perfect magnetic conductor implementations are also discussed. Numerical results in the realm of CPU time saving, asymmetry and numerical errors as well as specific absorption rate (SAR) of human skin are presented.

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Section: Averagingmentioning

confidence: 99%

“…The popularity of ADI-FDTD method has further brought about the successful extensions into modeling lossy media [4][5][6][7][8][9], while retaining its unconditional stability feature. The proof of unconditional stability feature for various ADI-FDTD schemes for lossy media has been provided in [10].…”

Section: Introductionmentioning

confidence: 99%

Unified Efficient Fundamental Adi-FDTD Schemes for Lossy Media

Heh¹,

Tan²

2011

PIER B

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“…By substituting the right-hand side (RHS) of (9b) into (9a) and after some manipulations, the implicit update of is performed as (15) With (15), a system of linear equations with tridiagonal coefficient matrix is formed and the update of is efficiently carried out. Subsequently the update of is determined as (16) Upon updating and , the updates of remaining field components are performed using the 4 explicit update (9c)-(9f). Note that at every field point on the Yee's grid, only one field component is directly available.…”

Section: Formulationmentioning

confidence: 99%

“…To overcome the CFL condition, several unconditionally stable FDTD methods have been developed based on techniques such as alternating direction implicit (ADI) [3], [4], split-step [5], [6], locally 1-D (LOD) [7]- [10] and Crank-Nicolson [11], [12]. Unconditionally stable FDTD methods have been extended to treat complex materials that are frequency dispersive [13], [14] and lossy [15], [16].…”

Section: Introductionmentioning

confidence: 99%

A Split-Step FDTD Method for 3-D Maxwell's Equations in General Anisotropic Media

Singh

Tan

Chen

2010

IEEE Trans. Antennas Propagat.

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A split-step finite-difference time-domain (FDTD) method is presented for 3-D Maxwell's equations in general anisotropic media. The general anisotropic media can be characterized by full permittivity and permeability tensors. Stability analysis of the proposed split-step FDTD method using the Fourier method is presented. The eigenvalues of the Fourier amplification matrix are numerically shown to have unity magnitude even for time steps greater than the Courant limit time step, thereby illustrating the stable and non-dissipative nature of the split-step FDTD method in general anisotropic media. Numerical results are presented to further validate the accuracy and stability of the proposed split-step FDTD method in general anisotropic media.Index Terms-Alternating direction implicit FDTD, anisotropic media, finite-difference time-domain (FDTD) method, locally 1-D FDTD, split-step FDTD, unconditionally stable FDTD methods.

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“…For example, it was proved by Fourier methods in [4]- [8] that the ADI-FDTD methods are unconditionally stable and have reasonable numerical dispersion error; Reference [9] studied the divergence property; Reference [10] studied ADI-FDTD in a perfectly matched medium; Reference [11] gave an efficient PML implementation for the ADI-FDTD method. By Poynting's theorem, Energy conservation is an important property for Maxwell equations and good numerical method should conform it.…”

Section: Introductionmentioning

confidence: 99%

Energy Identities of ADI-FDTD Method with Periodic Structure

Shi¹,

Yang

2015

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In this paper, a new kind of energy identities for the Maxwell equations with periodic boundary conditions is proposed and then proved rigorously by the energy methods. By these identities, several modified energy identities of the ADI-FDTD scheme for the two dimensional (2D) Maxwell equations with the periodic boundary conditions are derived. Also by these identities it is proved that 2D-ADI-FDTD is approximately energy conserved and unconditionally stable in the discrete L 2 and H 1 norms. Experiments are provided and the numerical results confirm the theoretical analysis on stability and energy conservation.

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Stability and Dispersion Analysis for ADI-FDTD Method in Lossy Media

Cited by 30 publications

References 17 publications

Unified Efficient Fundamental Adi-FDTD Schemes for Lossy Media

Unified Efficient Fundamental Adi-FDTD Schemes for Lossy Media

A Split-Step FDTD Method for 3-D Maxwell's Equations in General Anisotropic Media

Energy Identities of ADI-FDTD Method with Periodic Structure

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