2000 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

IEEE Transactions on Microwave Theory and Techniques
Volume 48 Number 6, June 2000

Table of Contents for this issue

Complete paper in PDF format

Integer Lattice Gas Automata for Computational Electromagnetics

Joanne R. Treurniet, Neil R. S. Simons and Greg E. Bridges Member, IEEE

Page 985.

Abstract:

Integer lattice gas automata (ILGA) are combined with the transmission-line matrix (TLM) method to yield a new electromagnetic-field computation algorithm using very low-precision integer variables. Lattice gas automata can be evaluated using look-up tables on special-purpose hardware and do not require floating-point arithmetic. In this paper, we present a TLM motivated ILGA with emphasis placed on algorithms that demonstrate minimal dissipation.

References

  1. C. Christopoulos, The Transmission Line Modeling Method (TLM), Piscataway, NJ: IEEE Press, 1993.
  2. B. Boghosian, "Lattice gases,"in 1989 Lectures in Complex Systems, SFI Studies in the Sciences of Complexity, E. Jen, Ed. Reading, MA: Addison-Wesley, 1990,vol. Lecture Vol. II.
  3. G. D. Doolen, U. Frisch, B. Hasslacher, S. Orszag, and S. Wolfram, Eds., Lattice Gas Methods for Partial Differential Equations, Santa Fe, NM: Santa Fe Inst., 1990.
  4. B. M. Boghosian, J. Yepez, F. J. Alexander and N. H. Margolus, "Integer lattice gases", Phys. Rev. E, vol. 55, pp.  4137-4147, 1997.
  5. N. Margolus, "CAM-8: a Computer architecture based on cellular automata,"in Pattern Formation and Lattice Gas Automata, Providence, RI: Amer. Math. Soc., 1995.
  6. P. Russer, "On the field theoretical foundation of the transmission line matrix method", presented at the 1st Int. TLM Modeling Workshop, Victora, B.C., Canada,1995.
  7. N. R. S. Simons and J. LoVetri, "Derivation of two-dimensional TLM algorithms on arbitrary grids using finite element concepts", presented at the 1st Int. TLM Modeling Workshop, Victoria, B.C., Canada,1995.
  8. N. R. S. Simons and A.-R. Sebak, "New transmission line matrix node for two-dimensional electromagnetic field problems", Canadian J. Phys. , vol. 69, pp.  1388-1398, 1991.
  9. U. Frisch, D. d'Humières, B. Hasslacher, P. Lallemand, Y. Pomeau and J.-P. Rivet, "Lattice gas hydrodynamics in two and three dimensions", Complex Syst., vol. 1, p.  599, 1987.
  10. G. E. Bridges and N. R. S. Simons, "Extremely low precision integer cellular array algorithm for computational electromagnetics", IEEE Microwave Guided Wave Lett., vol. 9, pp.  1-3, Jan.  1999.
  11. C. Alder, B. M. Boghosian, E. G. Flekkoy, N. Margolus and D. H. Rothman, "Simulating three-dimensional hydrodynamics on a cellular-automata machine", J. Statist. Phys., vol. 81, p.  105, 1995.
  12. D. d'Humières and P. Lallemand, "Numerical simulations of hydrodynamics with lattice gas automata in two dimensions", Complex Syst., vol. 1, pp.  599 -632, 1987.
  13. J. R. Treurniet, N. R. S. Simons, G. E. Bridges and M. Cuhaci, "Evaluation of dissipation within an ILGA for computational electromagnetics", Int. J. Numer. Modeling ,
  14. E. C. Jordan and K. G. Balmain, Electromagnetic Waves and Radiating Systems, Engelwood Cliffs, NJ: Prentice-Hall, 1968.
  15. W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing , Cambridge: U.K.: Cambridge Univ. Press, 1992.
  16. N. R. S. Simons, R. Siushansian, J. LoVetri and M. Cuhaci, "Comparison of the transmission line matrix and finite-difference time-domain methods for a problem containing a sharp metallic edge", IEEE Trans. Microwave Theory Tech.,
  17. P. B. Johns, "A symmetrical condensed node for the TLM method", IEEE Trans. Microwave Theory Tech., vol. MTT-35, pp.  370-377, 1987.
  18. N. R. S. Simons, G. E. Bridges and M. Cuhaci, "A lattice gas automaton capable of modeling three-dimensional electromagnetic fields", J. Comput. Phys., vol. 151, pp.  816-835, 1999.