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SPATIALLY WEIGHTED NUMERICAL MODELS FOR THE TWO-DIMENSIONAL WAVE EQUATION: FD ALGORITHM AND SYNTHESIS OF THE EQUIVALENT TLM MODEL.

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Title: SPATIALLY WEIGHTED NUMERICAL MODELS FOR THE TWO-DIMENSIONAL WAVE EQUATION: FD ALGORITHM AND SYNTHESIS OF THE EQUIVALENT TLM MODEL.
Authors: Simons, N. R. S.1, Sebak, A. A.1
Source: International Journal of Numerical Modelling. Feb93, Vol. 6 Issue 1, p47-65. 19p.
Subjects: Wave equation, Algorithms, Partial differential equations, Theory of wave motion, Electric lines, Mathematical models
Abstract: In this paper a new TLM model for the two-dimensional wave equation is introduced. It is synthesized directly from a FD algorithm. The FD algorithm is second-order-accurate in both space and time, and is explicitly time-stepped. The spatial derivatives in the FD algorithm are approximated by the weighted combination of two standard central difference stencils, one oriented as usual, the other rotated by 45° with its arms extended by a factor of (2)½. The TLM model is realized as the weighted connection of two original models (with the same geometrical configuration as the PD algorithm). The weighting in the TLM model is accomplished by using a variable intrinsic impedance for specific elemental transmission lines. The FD and TLM methods possess identical dispersion relations if the former is operated at its upper limit of stability. Therefore, under these conditions both represent identical models for the simulation of wave propagation. The propagation characteristics of the new model are investigated and the conditions for approximate numerical isotropy are provided. The numerical implementation (scattering matrix and transfer event) is described. To validate the new model, the calculation of cutoff frequencies of various modes in rectangular waveguide is performed. Comparison with analytical results (for an unfilled waveguide) and other numerical results (for a waveguide partially filled with a dielectric) validate the implementation of the model. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Numerical Modelling is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: SPATIALLY WEIGHTED NUMERICAL MODELS FOR THE TWO-DIMENSIONAL WAVE EQUATION: FD ALGORITHM AND SYNTHESIS OF THE EQUIVALENT TLM MODEL.
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  Data: <searchLink fieldCode="DE" term="%22Wave+equation%22">Wave equation</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Theory+of+wave+motion%22">Theory of wave motion</searchLink><br /><searchLink fieldCode="DE" term="%22Electric+lines%22">Electric lines</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink>
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  Data: In this paper a new TLM model for the two-dimensional wave equation is introduced. It is synthesized directly from a FD algorithm. The FD algorithm is second-order-accurate in both space and time, and is explicitly time-stepped. The spatial derivatives in the FD algorithm are approximated by the weighted combination of two standard central difference stencils, one oriented as usual, the other rotated by 45° with its arms extended by a factor of (2)½. The TLM model is realized as the weighted connection of two original models (with the same geometrical configuration as the PD algorithm). The weighting in the TLM model is accomplished by using a variable intrinsic impedance for specific elemental transmission lines. The FD and TLM methods possess identical dispersion relations if the former is operated at its upper limit of stability. Therefore, under these conditions both represent identical models for the simulation of wave propagation. The propagation characteristics of the new model are investigated and the conditions for approximate numerical isotropy are provided. The numerical implementation (scattering matrix and transfer event) is described. To validate the new model, the calculation of cutoff frequencies of various modes in rectangular waveguide is performed. Comparison with analytical results (for an unfilled waveguide) and other numerical results (for a waveguide partially filled with a dielectric) validate the implementation of the model. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of International Journal of Numerical Modelling is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1002/jnm.1660060106
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        Text: English
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        PageCount: 19
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        Type: general
      – SubjectFull: Algorithms
        Type: general
      – SubjectFull: Partial differential equations
        Type: general
      – SubjectFull: Theory of wave motion
        Type: general
      – SubjectFull: Electric lines
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      – SubjectFull: Mathematical models
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      – TitleFull: SPATIALLY WEIGHTED NUMERICAL MODELS FOR THE TWO-DIMENSIONAL WAVE EQUATION: FD ALGORITHM AND SYNTHESIS OF THE EQUIVALENT TLM MODEL.
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              Text: Feb93
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              Y: 1993
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