A method for algebraic analysis of the TLM algorithm

An analogy is described between the TLM algorithm and discrete state‐space control theory. The analogy is used to derive the characteristic equations corresponding to parametrized model structures. Characteristic equations corresponding to several widely used node structures are derived by this mean...

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Published inInternational journal of numerical modelling Vol. 8; no. 1; pp. 61 - 71
Main Authors Witwit, A. R. M., Wilkinson, A. J., Pulko, S. H.
Format Journal Article
LanguageEnglish
Published Sussex John Wiley & Sons, Ltd 01.01.1995
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ISSN0894-3370
1099-1204
DOI10.1002/jnm.1660080107

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Abstract An analogy is described between the TLM algorithm and discrete state‐space control theory. The analogy is used to derive the characteristic equations corresponding to parametrized model structures. Characteristic equations corresponding to several widely used node structures are derived by this means and found to be consistent with the observed behaviour of corresponding TLM models. An example is given of the use of the analogy in teh predictive mode.
AbstractList An analogy is described between the TLM algorithm and discrete state‐space control theory. The analogy is used to derive the characteristic equations corresponding to parametrized model structures. Characteristic equations corresponding to several widely used node structures are derived by this means and found to be consistent with the observed behaviour of corresponding TLM models. An example is given of the use of the analogy in teh predictive mode.
Author Witwit, A. R. M.
Pulko, S. H.
Wilkinson, A. J.
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Cites_doi 10.1002/nme.1620191012
10.1049/piee.1971.0217
10.1109/TMTT.1974.1128203
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Susan Pulko obtained a B.Sc. in physics together with an ARCS from Imperial College (London) in 1977. This was followed by a Ph.D. from the University of Nottingham in 1981. Her current research interests centre on the TLM algorithm and on its application to a range of physical processes, especially as applied to manufacturing. Current work involves development of the algorithm itself and TLM applications in the glass and ceramic industries.
Anthony James Wilkinson graduated from the niversity of Hull with a B.Sc. in Electronic Engineering in 1982 and a Ph.D. in adaptive control in 1987. He is currently a lecturer in the Department of Electronic Engineering where his research interests include TLM algorithms and computer control of magnetostrictive actuation.
Abdul Mehdi Witwit was born in Babylon in 1965. He graduated in Electronic Engineering from the Univeristy of Hull in 1990. He has recently submitted his Ph.D. thesis on the topic of meshing in TLM diffusion problems.
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References G. F. Franklin, J. D. Powell and M. L. Workman, Digital Control of Dynamic Systems, 2nd edn, Addison-Wesley, Wokingham, 1990.
N. R. S. Simons and A. A. Sebak, 'Spatially weighted numerical models for the 2-dimensional wave equation: FD algorithm and synthesis of the equivalent TLM model', Int. J. Numer. Modelling, 5, 111-130 (1992).
P. B. Johns, 'The solution of inhomogeneous waveguide problems using a transmission line matrix', IEEE Trans. Microwave Theory Techniques, MTT-22, 209-215 (1974).
P. B. Johns and G. Butler, 'The consistency and accuracy of the TLM method for diffusion and its relationship to existing methods', Int. J. Numer. Methods in Eng., 19, 1549-1554 (1983).
R. H. Middleton and G. C. Goodwin, Digital Control and Estimation, a Unified Approach, Prentice Hall, Englewood Cliffs, NJ, 1990.
P. B. Johns and R. L. Beurle, 'Numerical solution of 2-demensional scattering problems using a transmission line matrix', Proc. IEE, 118, 1203-1208 (1971).
1990
1986
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Franklin G. F. (e_1_2_1_4_2) 1990
References_xml – reference: R. H. Middleton and G. C. Goodwin, Digital Control and Estimation, a Unified Approach, Prentice Hall, Englewood Cliffs, NJ, 1990.
– reference: N. R. S. Simons and A. A. Sebak, 'Spatially weighted numerical models for the 2-dimensional wave equation: FD algorithm and synthesis of the equivalent TLM model', Int. J. Numer. Modelling, 5, 111-130 (1992).
– reference: G. F. Franklin, J. D. Powell and M. L. Workman, Digital Control of Dynamic Systems, 2nd edn, Addison-Wesley, Wokingham, 1990.
– reference: P. B. Johns and G. Butler, 'The consistency and accuracy of the TLM method for diffusion and its relationship to existing methods', Int. J. Numer. Methods in Eng., 19, 1549-1554 (1983).
– reference: P. B. Johns and R. L. Beurle, 'Numerical solution of 2-demensional scattering problems using a transmission line matrix', Proc. IEE, 118, 1203-1208 (1971).
– reference: P. B. Johns, 'The solution of inhomogeneous waveguide problems using a transmission line matrix', IEEE Trans. Microwave Theory Techniques, MTT-22, 209-215 (1974).
– year: 1990
– volume: 5
  start-page: 111
  year: 1992
  end-page: 130
  article-title: Spatially weighted numerical models for the 2‐dimensional wave equation: FD algorithm and synthesis of the equivalent TLM model
  publication-title: Int. J. Numer. Modelling
– volume: MTT‐22
  start-page: 209
  year: 1974
  end-page: 215
  article-title: The solution of inhomogeneous waveguide problems using a transmission line matrix
  publication-title: IEEE Trans. Microwave Theory Techniques
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  year: 1986
  end-page: 218
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  year: 1971
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  article-title: Numerical solution of 2‐demensional scattering problems using a transmission line matrix
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  year: 1983
  end-page: 1554
  article-title: The consistency and accuracy of the TLM method for diffusion and its relationship to existing methods
  publication-title: Int. J. Numer. Methods in Eng.
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  doi: 10.1002/nme.1620191012
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  article-title: Spatially weighted numerical models for the 2‐dimensional wave equation: FD algorithm and synthesis of the equivalent TLM model
  publication-title: Int. J. Numer. Modelling
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  doi: 10.1049/piee.1971.0217
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