Toward the construction of a fourth-order difference scheme for transient EM wave simulation: staggered grid approach

Young, Jeffrey L.; Gaitonde, Datta V.; Shang, J. S.

doi:10.1109/8.650067

Cited by 128 publications

(80 citation statements)

References 14 publications

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“…(13), the one-sided derivatives involved in Eq. (13) are approximated in the BPS method [39,40] by using all fictitious and original grid points in the same subdomain,…”

Section: A Methods Of Derivative Matching With Fictitious Pointsmentioning

confidence: 99%

“…Thus, the IDM yields an excellent way to generalize the embedding FDTD scheme to high orders. Furthermore, it could be applied together with various different high-order time-domain methods, such as high-order FDTD methods [3,[10][11][12][13][14][15][16], the MRTD method [17,18], and the LSTD method [24][25][26]. In these applications, the number of FPs (m) could be simply specified according to the length of stencil involved in these time-domain methods, and significant improvement of accuracy is expected.…”

Section: Referring Tomentioning

confidence: 99%

“…For broadband applications and problems including material interface, wave scattering and penetration over large and complex domains, the grid size required by using the FDTD method could become prohibitively expensive for modern computers. Much progress has been made in the past two decades in improving the FDTD method, including plentiful methods for removing the staircased approximation for boundaries and geometries, [5][6][7][8][9] and numerous high-order FDTD methods [3,[10][11][12][13][14][15][16]. Here, by high order we refer to orders being higher than three, which are essential for modern problems of moderately high frequency (short) waves and/or large domain in nature.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces

Zhao

Wang

2004

Journal of Computational Physics

196

164

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This paper introduces a series of novel hierarchical implicit derivative matching methods to restore the accuracy of high-order finite difference time-domain (FDTD) schemes of computational electromagnetics (CEM) with material interfaces in one (1D) and two spatial dimensions (2D). By making use of fictitious points, systematic approaches are proposed to locally enforce the physical jump conditions at material interfaces in a preprocessing stage, to arbitrarily high orders of accuracy in principle. While often limited by numerical instability, orders up to 16 in 1D and 2D are achieved. Detailed stability analyses are presented for the present approach to examine the up limit in constructing embedded FDTD methods. As natural generalizations of the high-order FDTD schemes, the proposed derivative matching methods automatically reduce to the standard FDTD schemes when the material interfaces are absent. An interesting feature of the present approach is that it encompasses a variety of schemes of different orders in a single code. Another feature of the present approach is that it can be robustly implemented with other high accuracy time-domain approaches, such as the multiresolution time-domain (MRTD) method and the local spectral time-domain (LSTD) method, to cope 1 with material interfaces. Numerical experiments on both 1D and 2D problems are carried out to test the convergence, examine the stability, access the efficiency, and explore the limitation of the proposed methods. It is found that operating at their best capacity, the proposed high order schemes are at least a million times more efficient than their fourth order versions in both 1D and 2D. Therefore, it is believed that the proposed hierarchical derivative matching methods are highly accurate, efficient, and robust for CEM.

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“…(13), the one-sided derivatives involved in Eq. (13) are approximated in the BPS method [39,40] by using all fictitious and original grid points in the same subdomain,…”

Section: A Methods Of Derivative Matching With Fictitious Pointsmentioning

confidence: 99%

Section: Referring Tomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces

Zhao

Wang

2004

Journal of Computational Physics

196

164

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show abstract

“…An interior scheme can be realized with explicit (as done in this paper) or implicit [see Young et al, 1997] stencils. This interior scheme in conjunction with the efficient, high-order integrator presented herein gives rise to a conditionally stable algorithm, provided that the domain is periodic.…”

Section: Discussionmentioning

confidence: 99%

High‐order, leapfrog methodology for the temporally dependent Maxwell's equations

Young¹

2001

Radio Science

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Abstract.A high-order, leapfrog integrator is presented and analyzed for Maxwell's time domain equations. The integrator is shown to be quite robust in terms of its efficiency and memory demands. Moreover, the integrator retains the original simplicity of the traditional second-order, leapfrog integrator. Rigorous Fourier analyses are presented to quantify the dispersion, dissipation, and stability properties of the integrator. To limit the scope of the presentation, the 2x2, 2x4, 4x2, and 4x4 schemes are examined and compared. Here the first digit denotes temporal accuracy; the second digit denotes spatial accuracy. Numerical demonstrations, using the three-dimensional rectangular waveguide as the object under test, are provided to further substantiate the theoretical analysis.

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“…Among existing numerical techniques, the finite-difference timedomain (FDTD) method has a wide applicability in many areas of research [5]. Higher order (HO) 3-D FDTD methodology to be a powerful numerical method for such complex and multiple materials structures simulation [6][7][8][9]. Furthermore, the development of high power microwave antenna, aviation and space techniques has motivated the interest in electromagnetic scattering problems involving combinative objects [10,20].…”

Section: Introductionmentioning

confidence: 99%

Time Domain Physical Optics for the Higher-Order FDTD Modeling in Electromagnetic Scattering From 3-D Complex and Combined Multiple Materials Objects

Faghihi¹,

Heydari

2009

PIER

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Abstract-This paper proposes a hybrid methodology that combines an extended form of Finite-Deference Time-Domain (FDTD) method with Time Domain Physical Optics (TDPO) for analysis of 3-D scattering of combinative objects in complex electromagnetic compatibility (EMC) problems. Establishing a covariant formulation for FDTD, the extended algorithm introduces a parametric topology of accurate nonstandard schemes for the non-orthogonal div-curl problem and the suppression of lattice dispersion. For complex-combined objects including a small size (SS) and large size (LS) parts, using TDPO is an appropriate approach for coupling between two regions. Thus, our technique solves the EMC complexity with the help of higher order FDTD (HOFDTD) and the combinatory structures by using the TDPO. Numerical validation confirms the superiority of the proposed algorithm via realistic EMC applications.

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Toward the construction of a fourth-order difference scheme for transient EM wave simulation: staggered grid approach

Cited by 128 publications

References 14 publications

High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces

High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces

High‐order, leapfrog methodology for the temporally dependent Maxwell's equations

Time Domain Physical Optics for the Higher-Order FDTD Modeling in Electromagnetic Scattering From 3-D Complex and Combined Multiple Materials Objects

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