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Subspace Trajectory Piecewise-Linear Model Order Reduction for Nonlinear Circuits

Published online by Cambridge University Press:  03 June 2015

Xiaoda Pan ,
Hengliang Zhu ,
Fan Yang  and
Xuan Zeng
Xiaoda Pan*
Affiliation:
State Key Lab. of ASIC & System, Microelectronics Department, Fudan University, Shanghai, P.R. China
Hengliang Zhu*
Affiliation:
State Key Lab. of ASIC & System, Microelectronics Department, Fudan University, Shanghai, P.R. China
Fan Yang*
Affiliation:
State Key Lab. of ASIC & System, Microelectronics Department, Fudan University, Shanghai, P.R. China
Xuan Zeng*
Affiliation:
State Key Lab. of ASIC & System, Microelectronics Department, Fudan University, Shanghai, P.R. China
*
Corresponding author.Email:hlzhu@fudan.edu.cn
Email:082052014@fudan.edu.cn
Email:yangfan@fudan.edu.cn
Email:xzeng@fudan.edu.cn
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Abstract

Despite the efficiency of trajectory piecewise-linear (TPWL) model order reduction (MOR) for nonlinear circuits, it needs large amount of expansion points for large-scale nonlinear circuits. This will inevitably increase the model size as well as the simulation time of the resulting reduced macromodels. In this paper, subspace TPWL-MOR approach is developed for the model order reduction of nonlinear circuits. By breaking the high-dimensional state space into several subspaces with much lower dimensions, the subspace TPWL-MOR has very promising advantages of reducing the number of expansion points as well as increasing the effective region of the reduced-order model in the state space. As a result, the model size and the accuracy of the TWPL model can be greatly improved. The numerical results have shown dramatic reduction in the model size as well as the improvement in accuracy by using the subspace TPWL-MOR compared with the conventional TPWL-MOR approach.

Keywords

94C0593A1568U0768U2041A21Trajectory piecewise linear model order reductionnonlinear circuits
Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 3 , September 2013 , pp. 639 - 663
Copyright
Copyright © Global Science Press Limited 2013

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References

[1]Pillage, L. and Rohrer, R., Asymptotic waveform evaluation for timing analysis, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 9, no. 4, pp. 352–366, April 1990.Google Scholar
[2]Feldman, P. and Freund, R., Efficient linear circuit analysis by Padé approximation via the Lanczos process, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 14, no. 5, pp. 639–649, May 1995.CrossRefGoogle Scholar
[3]Odabasioglu, A., Celik, M., and Pileggi, L., PRIMA: Passive reduced-order interconnect macromodeling algorithm, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 17, no. 8, pp. 645–654, Aug. 1998.Google Scholar
[4]Freund, R., SPRIM: Structure-preserving reduced-order interconnect macromodeling, in Proceedings of IEEE/ACM International Conference on Computer-Aided Design, Nov. 2004, pp. 80–87.Google Scholar
[5]Phillips, J. R., Projection frameworks for model reduction of weakly nonlinear systems, in Proceedings of IEEE/ACM Design Automation Conference, 2000, pp. 184–189.Google Scholar
[6]Rewienski, M. and White, J., A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, pp. 155–170, Feb. 2003.Google Scholar
[7]Gu, C., Model order reduction of nonlinear dynamical systems, Dissertation, University of California, Berkeley, 2011.Google Scholar
[8]Vasilyev, D., Rewienski, M., and White, J., A TBR-based trajectory piecewise-linear algorithm for generating accurate low-order models for nonlinear analog circuits and MEMS, in Proceedings of IEEE/ACM Design Automation Conference, 2003, pp. 490–495.Google Scholar
[9]Gu, C. and Roychowdhury, J., ManiMOR: Model reduction via projection onto nonlinear manifolds, with applications to analog circuits and biochemical systems, in Proceedings of the IEEE International Conference on Computer-Aided Design, pp. 85–92, Nov. 2008.Google Scholar
[10]Vasilyev, D., Rewienski, M., and White, J., Perturbation analysis of TBR model reduction in applicationtotrajectory-piecewise linear algorithm for MEMS structures, in NSTI Nanotech-nology Conference, vol. 2, 2004, pp. 434–437.Google Scholar
[11]Wang, Y., Song, H., Pant, K., Peabody, H., Ku, J., and Butler, C. D., A projection-based model order reduction simulation tool for spacecraft thermal analysis, in Thermal and Fluids Analysis Workshop, Aug. 2011.Google Scholar
[12]Gratton, D. and Willcox, K., Reduced-order, trajectory piecewise-linear models for nonlinear computational fluid dynamics, in 34th AIAA Fluid Dynamic Conference, June 2004.CrossRefGoogle Scholar
[13]Cardoso, M. A. and Durlofsky, L. J., Linearized reduced-order models for subsurface flow simulation, Journal of Computational Physics, vol. 229, pp. 681–700, February 2010.CrossRefGoogle Scholar
[14]Long, C., Simonson, L., Liao, W., and He, L., Microarchitecture configurations and floorplan-ning co-optimization, IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 15, pp. 830–841, July 2007.Google Scholar
[15]Long, C., Simonson, L., Liao, W., and He, L., Floorplanning optimization with trajectory piecewise-linear model for pipelined interconnects, in Proceedings of IEEE/ACM Design Automation Conference, July 2004, pp. 640–645.Google Scholar
[16]Lai, X. and Roychowdhury, J., TP-PPV: Piecewise nonlinear, time-shifted oscillator macromodel extraction for fast, accurate PLL simulation, in IEEE/ACM International Conference on Computer-Aided Design, November 2006, pp. 269–274.Google Scholar
[17]Yu, H., Liu, X., Wang, H., and Tan, S. X.-D., A fast analog mismatch analysis by an incremental and stochastic trajectory piecewise linear macromodel, in 2010 15th Asia and South Pacific Design Automation Conference (ASP-DAC), January 2010, pp. 211–216.Google Scholar
[18]Dong, N. and Roychowdhury, J., General-purpose nonlinear model-order reduction using piecewise-polynomial representations, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 27, no. 2, pp. 249–264, February 2008.Google Scholar
[19]Dong, N. and Roychowdhury, J., Piecewise polynomial nonlinear model reduction, in Proceedings of IEEE/ACM Design Automation Conference, Jun. 2003, pp. 484–489.Google Scholar
[20]Zong, K., Yang, F., and Zeng, X., A wavelet-collocation-based trajectory piecewise-linear algorithm for time-domain model-order reduction of nonlinear circuits, IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 57, pp. 2981–2990, November 2010.Google Scholar
[21]Pan, X., Yang, F., Zeng, X., and Su, Y., An efficient transistor-level piecewise-linear macromod-eling approach for model order reduction of nonlinear circuits, in Design, Automation and Test in Europe Conference, March 2010, pp. 1673–1676.Google Scholar
[22]Amorocho, J. P. and Fabbender, H., Time dependent weight functions for the trajectory piecewise-linear approach, in European Conference on Mathematics for Industry, vol. 2, July 2010, pp. 434–437.Google Scholar
[23]Bond, B. N. and Daniel, L., Stabilizing schemes for piecewise-linear reduced order models via projection and weighting functions, in Proceedings of the IEEE International Conference on Computer-Aided Design, pp. 860–867, 2007.Google Scholar
[24]Bechtold, T., Striebel, M., Mohaghegh, K., and Maten, E., Nonlinear model order reduction in nanoelectronics: Combination of POD and TPWL, PAMM, vol. 8, pp. 10057–10060, 2008.CrossRefGoogle Scholar
[25]Tiwary, S. K. and Rutenbar, R. A., Faster, parametric trajectory-based macromodel via localized linear reductions, in IEEE/ACM International Conference on Computer-Aided Design, November 2006, pp. 876–883.Google Scholar
[26]Gu, C. and Roychowdhury, J., Manifold construction and parameterization for nonlinear manifold-based model reduction, in Proceedings of the IEEE Asia and South-Pacific Design Automation Conference, pp. 205–210, 2010.Google Scholar
[27]Gu, C., QLMOR: A projection-based nonlinear model order reduction approach using quadratic-linear representation of nonlinear systems, IEEE Transaction on Computer-Aided Design of Integrated Circuits and Systems, vol. 30, no. 9, pp. 1307–1320, Sep. 2011.Google Scholar
[28]Foo, J. and Karniadakis, G. E., Multi-element probabilistic collocation method in high dimensions, Journal of Computation Physics, vol. 229, pp. 1536–1557, 2010.Google Scholar
[29]Ho, C.-W., Ruehli, A. E., and Brennan, P. A., The modified nodal approachto network analysis, IEEE Transactions on Circuits and Systems, vol. 22, pp. 504–509, June 1975.Google Scholar
[30]Yang, F., Zeng, X., Su, Y., and Zhou, D., RLCSYN: RLC equivalent circuit synthesis for structure-preserved reduced-order model of interconnect, in IEEE International Symposium on Circuits and Systems, May 2007, pp. 2710–2713.Google Scholar
[31]Su, Y., Yang, F., Zeng, X., AMOR: An efficient aggregating based model order reduction method for many-terminal interconnect circuits, ACM/IEEE Design Automation Conference, pp. 295–300, Jun. 2012.Google Scholar