Table of Contents
ISRN Applied Mathematics
Volume 2011 (2011), Article ID 610637, 7 pages
http://dx.doi.org/10.5402/2011/610637
Research Article

Powering Multiparameter Homotopy-Based Simulation with a Fast Path-Following Technique

1Electronic Instrumentation and Atmospheric Sciences School, University of Veracruz, 91000 Xalapa, VER, Mexico
2Institute of Physics, Autonomous University of San Luis Potosi, 78000 San Luis Potosi, SLP, Mexico
3Electronics Department, National Institute for Astrophysics, Optics and Electronics, 72000 Tonantzintla, PUE, Mexico

Received 30 June 2011; Accepted 23 August 2011

Academic Editors: F. Jauberteau and C. I. Siettos

Copyright © 2011 Héctor Vázquez-Leal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. B. Goldgeisser and M. M. Green, “A method for automatically finding multiple operating points in nonlinear circuits,” IEEE Transactions on Circuits and Systems-I, vol. 52, no. 4, pp. 776–784, 2005. View at Publisher · View at Google Scholar
  2. R. C. Melville and L. Trajković, “Artificial parameter homotopy methods for the DC operating point problem,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 12, no. 6, pp. 861–877, 1997. View at Google Scholar
  3. L. Trajković, R. C. Melville, and S. C. Fang, “Passivity and no-gain properties establish global convergence of a homotopy method for DC operating points,” in Proceedings of the IEEE International Symposium on Circuits and Systems, 1990. View at Scopus
  4. H. Vázquez-Leal, L. Hernández-Martínez, and A. Sarmiento-Reyes, “Double-bounded homotopy for analysing nonlinear resistive circuits,” in Proceedings of the IEEE International Symposium on Circuits and Systems, May 2005. View at Publisher · View at Google Scholar · View at Scopus
  5. J. S. Roychowdhury and R. C. Melville, “Homotopy techniques for obtaining a DC solution of large-scale MOS circuits,” in Proceedings of the 33rd Annual Design Automation Conference, 1996. View at Scopus
  6. C. T. Kelley, Solving Nonlinear Equations with Newton’s Method, Fundamentals of Algorithms, SIAM, Philadelphia, Pa, USA, 2003.
  7. D. M. Wolf and S. R. Sanders, “Multiparameter homotopy methods for finding DC operating points of nonlinear circuits,” IEEE Transactions on Circuits and Systems-I, vol. 43, no. 10, pp. 824–838, 1996. View at Publisher · View at Google Scholar
  8. J. Roychowdhury and R. Melville, “Delivering global DC convergence for large mixed-signal circuits via homotopy/continuation methods,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 25, no. 1, pp. 66–78, 2006. View at Publisher · View at Google Scholar · View at Scopus
  9. H. Vázquez-Leal, L. Hernández-Martínez, A. Sarmiento-Reyes, and R. S. Murphy-Arteaga, “Improving multi-parameter homotopy via symbolic analysis techniques for circuit simulation,” in Proceedings of the European Conference on Circuit Theory and Design, vol. 2, pp. 402–405, 2003.
  10. H. Vázquez-Leal, L. Hernández-Martínez, and A. Sarmiento-Reyes, “Numerical continuation scheme for tracing the double bounded homotopy for analysing nonlinear circuits,” in Proceedings of the International Conference on Communications, Circuits and Systems, 2005. View at Scopus
  11. E. L. Allgower and K. Georg, Numerical Path Following, 1994.
  12. K. Yamamura, “Simple algorithms for tracing solution curves,” IEEE Transactions on Circuits and Systems I, vol. 40, no. 8, pp. 537–541, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  13. M. Sosonkina, L. T. Watson, and D. E. Stewart, “Note on the end game in homotopy zero curve tracking,” ACM Transactions on Mathematical Software, vol. 22, no. 3, pp. 281–287, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. A. Ushida and L. O. Chua, “Tracing solution curves of nonlinear equations with sharp turning points,” International Journal of Circuit Theory and Applications, vol. 12, no. 1, pp. 1–21, 1984. View at Publisher · View at Google Scholar