QLMOR: A projection-based nonlinear model order reduction approach using quadratic-linear representation of nonlinear systems

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

Volumn 30, Issue 9, 2011, Pages 1307-1320

  Gu, Chenjie ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Model order reduction; nonlinear; projection; quadratic linear

Indexed keywords

DIFFERENTIAL ALGEBRAIC EQUATIONS; MODEL ORDER REDUCTION; MOMENT CALCULATION; MOMENT-MATCHING; NON-LINEAR MODEL; NONLINEAR; NONLINEAR KERNELS; NONLINEAR ORDINARY DIFFERENTIAL EQUATION; NUMERICAL STABILITIES; PIECEWISE LINEAR; PROJECTION; QUADRATIC NONLINEARITIES; QUADRATIC-LINEAR; REDUCED MODEL; REDUCED-ORDER MODELING; REDUCTION TECHNIQUES; TRAJECTORY-BASED; VOLTERRA ANALYSIS; VOLTERRA KERNELS;

ALGEBRA; COMPUTATIONAL COMPLEXITY; CONTROL NONLINEARITIES; LINEAR SYSTEMS; NONLINEAR SYSTEMS; ORDINARY DIFFERENTIAL EQUATIONS; STABILITY;

NONLINEAR EQUATIONS;

EID: 80052075715     PISSN: 02780070     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCAD.2011.2142184     Document Type: Article

References (27)

1. P. Li and L. Pileggi, "Compact reduced-order modeling of weakly nonlinear analog and RF circuits, " IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol. 24, no. 2, pp. 184-203, Feb. 2005. (Pubitemid 40178518)
2. J. Roychowdhury, "Reduced-order modelling of time-varying systems, " IEEE Trans. Circuits Syst.-II: Analog Digital Signal Process., vol. 46, no. 10, pp. 1273-1288, Oct. 1999.
3. J. R. Phillips, "Projection-based approaches for model reduction of weakly nonlinear time-varying systems, " IEEE Trans. Comput.-Aided Des., vol. 22, no. 2, pp. 171-187, Feb. 2003.
4. M. Rewienski and J. White, "A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices, " IEEE Trans. Comput.-Aided Des., vol. 22, no. 2, pp. 155-170, Feb. 2003.
5. C. Gu and J. Roychowdhury, "ManiMOR: Model reduction via projection onto nonlinear manifolds, with applications to analog circuits and biochemical systems, " in Proc. IEEE Int. Conf. Comput. Aided Des., Nov. 2008, pp. 85-92.
6. E. Grimme, "Krylov projection methods for model reduction, " Ph. D. dissertation, Dept. Electric. Eng., Univ. Illinois Urbana-Champaign, Urbana, 1997.
7. L. Pillage and R. Rohrer, "Asymptotic waveform evaluation for timing analysis, " IEEE Trans. Comput.-Aided Des., vol. 9, no. 4, pp. 352-366, Apr. 1990. (Pubitemid 20677959)
8. P. Feldmann and R. Freund, "Efficient linear circuit analysis by Padé approximation via the Lanczos process, " IEEE Trans. Comput.-Aided Des., vol. 14, no. 5, pp. 639-649, May 1995.
9. A. Odabasioglu, M. Celik, and L. Pileggi, "PRIMA: Passive reducedorder interconnect macromodelling algorithm, " in Proc. IEEE Int. Conf. Comput.-Aided Des., Nov. 1997, pp. 58-65.
10. J. Phillips, L. Daniel, and L. Silveira, "Guaranteed passive balancing transformations for model order reduction, " IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol. 22, no. 8, pp. 1027-1041, Aug. 2003.
11. Z. Bai and D. Skoogh, "Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems, " Appl. Numeric. Math., vol. 43, nos. 1-2, pp. 9-44, 2002. (Pubitemid 35022895)
12. L. Daniel and J. R. Phillips, "Model order reduction for strictly passive and causal distributed systems, " in Proc. IEEE Des. Automat. Conf., Aug. 2002, pp. 46-51.
13. S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering. New York: Perseus Books Group, Jan. 2001.
14. L. Chua, "The genesis of Chua's circuit, " Dept. Electric. Eng. Comput. Sci., Univ. California, Berkeley, Tech. Rep. UCB/ERL M92/1, 1992.
15. W. Rugh, Nonlinear System Theory: The Volterra-Wiener Approach. Baltimore, MD: Johns Hopkins Univ. Press, 1981.
16. S. Ravindran, "Proper orthogonal decomposition in optimal control of fluids, " Langley Res. Center, NASA, Hampton, VA, Tech. Rep. TM-1999-209113, Mar. 1999.
17. M. Rathinam and L. R. Petzold, "A new look at proper orthogonal decomposition, " SIAM J. Numeric. Anal., vol. 41, no. 5, pp. 1893-1925, 2003.
18. S. Tiwary and R. Rutenbar, "Faster, parametric trajectory-based macromodels via localized linear reductions, " in Proc. IEEE Int. Conf. Comput.-Aided Des., Nov. 2006, pp. 876-883.
19. B. N. Bond and L. Daniel, "Stabilizing schemes for piecewise-linear reduced order models via projection and weighting functions, " in Proc. IEEE Int. Conf. Comput.-Aided Des., Nov. 2007, pp. 860-867.
20. N. Dong and J. Roychowdhury, "General-purpose nonlinear modelorder reduction using piecewise-polynomial representations, " IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol. 27, no. 2, pp. 249-264, Feb. 2008. (Pubitemid 351169640)
21. C. Gu, "QLMOR: A new projection-based approach for nonlinear model order reduction, " in Proc. IEEE Int. Conf. Comput.-Aided Des., Nov. 2009, pp. 389-396.
22. J. Phillips, "Projection frameworks for model reduction of weakly nonlinear systems, " in Proc. IEEE Des. Automat. Conf., Jun. 2000, pp. 184-189.
23. D. Garfinkel, L. Garfinkel, M. Pring, B. Green, S. B. Chance, "Computer applications to biochemical kinetics, " Annu. Rev. Biochem., vol. 39, no. 1, pp. 473-498, 1970.
24. T. Sakurai and A. Newton, "Alpha-power law MOSFET model and its applications to CMOS inverter delay and other formulas, " IEEE J. Solid-State Circuits, vol. 25, no. 2, pp. 584-594, Apr. 1990. (Pubitemid 20701405)
25. J. Phillips, "Model reduction of time-varying linear systems using approximate multipoint Krylov-subspace projectors, " in Proc. IEEE Int. Conf. Comput.-Aided Des., Nov. 1998, pp. 96-102.
26. S. Sastry, Nonlinear Systems: Analysis, Stability and Control. New York: Springer, 1999.
27. G. Hachtel, R. Brayton, and F. Gustavson, "The sparse tableau approach to network analysis and design, " IEEE Trans. Circuit Theory, vol. 18, no. 1, pp. 101-113, Jan. 1971.