Dispersion of homogeneous and inhomogeneous waves in the Yee finite-difference time-domain grid

Schneider, John B.; Kruhlak, Robert J.

doi:10.1109/22.903087

Cited by 34 publications

(28 citation statements)

References 7 publications

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“…We know that the same relationship between the wavenumbers and the frequency results when we use the classical incident wave-source conditions [15] to generate a propagating plane-wave at a desired frequency. We note that the ADI-FDTD dispersion relation predicts two 3 It can be shown that when the real part of the complex frequency is the Nyquist frequency, its imaginary part admits both negative and positive values, the positive values causing the well-known unstable behavior of Yee-FDTD over the Courant limit [9], [13], [14] solutions with different wavenumbers for a given frequency at high Courant numbers: two are possible for some in the ADI-FDTD curve in Fig. 1[bottom]: the usual one with positive group velocity, and an anomalous one with negative group velocity.…”

Section: Group Velocitymentioning

confidence: 99%

On the dispersion relation of ADI-FDTD

Garcia

Rubio

Bretones

et al. 2006

IEEE Microw. Wireless Compon. Lett.

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Section: Group Velocitymentioning

confidence: 99%

On the dispersion relation of ADI-FDTD

Garcia

Rubio

Bretones

et al. 2006

IEEE Microw. Wireless Compon. Lett.

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“…We note that the superluminal wave vector components discussed in [9,13] are not incorporated in the results to be shown later. These components, which occur at the coarsest discretizations supported by the grid, experience exponential decay as they propagate.…”

Section: N=0mentioning

confidence: 99%

“…As discussed in [13], the critical angle in the FDTD world differs from that in the continuous world and is, in fact, a function of frequency. Nevertheless, we will refer to the critical angle as if it were a constant.…”

Section: Incidence Beyond the Critical Anglementioning

confidence: 99%

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Time-Domain Simulations of Problems in Ocean Acoustics

Schneider¹

2006

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The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the d-ataneeded, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports 10704-01881, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid DMB control number. A total-field scattered-field (TFSF) boundary can be used to introduce incident plane waves into finite-difference time-domain (FDTD) simulations. For fields which are traveling obliquely to the grid axes, there is no simple way to account fully for the effects of the inherent numerical artifacts associated with plane-wave propagation in the FDTD grid. Failure to account for these artifacts causes erroneous fields to leak across the TFSF boundary. The work performed under this grant developed a TFSF boundary for problems involving a planar interface that is theoretically exact. Such a boundary is essential when modeling the scattering from objects in the vicinity of ocean sediment. Although the TFSF boundary assumes a planar interface, the actual interface used in a simulation can take any shape and the space within the total-field region is arbitrary. A suite of C programs was written to implement the boundary. factual summary of the most significant information. PLEASE DO NOT5e. TASK NUMBER. Enter all task numbers as they 15. SUBJECT TERMS. Key words or phrases appear in the report, e.g. 05; RF0330201; T4112.identifying major concepts in the report.5f. WORK UNIT NUMBER. Enter all work unit numbers as they appear in the report, e.g. 001; 16. SECURITY CLASSIFICATION. Enter security AFAPL30480105.classification in accordance with security classification regulations, e.g. U, C, S, etc. If this form contains 6. AUTHOR(S). Enter name(s) of person(s) classified information, stamp classification level on the responsible for writing the report, performing the top and bottom of this page. research, or credited with the content of the report. The form of entry is the last name, first name, middle 17. LIMITATION OF ABSTRACT. This block must be initial, and additional qualifiers separated by commas, completed to assign a distribution limitation to the e.g. Smith, Richard, J, Jr.abstract. Enter UU (Unclassified Unlimited) or SAR (Same as Report). An entry in this block is necessary if 7. PERFORMING ORGANIZATION NAME(S) AND teasrc st elmtd the abstract is to be limited. Abstract A total-field scattered-field (TFSF) boundary can be used to introduce incident plane waves into fi...

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“…Decaying field in an absorbing or transparent medium is excited usually after refraction of a wave (or after its total internal reflection) on a plane boundary with the other transparent medium, owing to that decay appears only in one spatial direction, which is orthogonal to the interface, but in parallel direction, wave amplitude does not vary. Hence, in practice, the presence of decay causes appearance of inhomogeneous waves, whose constant phase surfaces are not parallel to the constant amplitude ones [16]. Formal introducing a complex-valued angle of incidence does not allow simulation of propagation for such waves, and here, one should use the representation of diffraction solution in terms of the parameters of wave propagation in the various coordinate axes, which can be complex simultaneously or separately.…”

Section: Introductionmentioning

confidence: 99%

Diffraction of a Plane Inhomogeneous Electromagnetic Wave by a Perfectly Conducting Half-Plane in an Absorbing Medium

Serdyuk

2013

AJEA

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Abstract:The Sommerfeld's problem of plane wave diffraction by a perfectly conducting half-plane is considered for the general case of an absorbing medium and an inhomogeneous incident wave, whose the constant phase planes are not parallel to the constant amplitude ones. The exact solution is represented in terms of parameters of incident wave propagation in the coordinate axes, but not in terms of angular variables, as usually. We adduce the original derivation of this solution, which use generalized functions and admits complex values for propagation parameters. Our approach is based on calculation of diffraction integrals by the method of transformations on the real axis without using a complex argument of integration. The results of diffraction field computation for the cases of an absorbing medium and of a decaying incident wave in a transparent medium are presented.

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Dispersion of homogeneous and inhomogeneous waves in the Yee finite-difference time-domain grid

Cited by 34 publications

References 7 publications

On the dispersion relation of ADI-FDTD

On the dispersion relation of ADI-FDTD

Time-Domain Simulations of Problems in Ocean Acoustics

Diffraction of a Plane Inhomogeneous Electromagnetic Wave by a Perfectly Conducting Half-Plane in an Absorbing Medium

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