Reduction of large circuit models via low rank approximate gramians

• Autorzy: Jing-Rebecca Li , Jacob White
• Języki publikacji: EN

Abstrakty

EN

We describe a model reduction algorithm which is well-suited for the reduction of large linear interconnect models. It is an orthogonal projection method which takes as the projection space the sum of the approximate dominant controllable subspace and the approximate dominant observable subspace. These approximate dominant subspaces are obtained using the Cholesky Factor ADI (CF-ADI) algorithm. We describe an improvement upon the existing implementation of CF-ADI which can result in significant savings in computational cost. We show that the new model reduction method matches moments at the negative of the CF-ADI parameters, and that it can be easily adapted to allow for DC matching, as well as for passivity preservation for multi-port RLC circuit models which come from modified nodal analysis.

Słowa kluczowe

EN

Lyapunov equations; moment matching; passivity; model reduction; Cholesky-Factor ADI

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2001
• Tom: 11
• Numer: 5
• Strony: 1151-1171

Daty

wydano

2001

Twórcy

autor

Jing-Rebecca Li

• Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, Room 1118, New York, NY 10012-1185, U.S.A.

autor

Jacob White

• Research Laboratory of Electronics, Massachusetts Institute of Technology, Room 36-817, Cambridge, MA 02139-4307, U.S.A.

Bibliografia

• Chandrasekharan P.C. (1996): Robust Control of Linear Dynamical Systems. — London: Harcourt Brace.
• Ellner N.S. and Wachspress E.L. (1991): Alternating direction implicit iteration for systems with complex spectra. — SIAM J. Numer. Anal., Vol.28, No.3, pp.859–870.
• Enns D.F. (1984): Model reduction with balanced realizations: An error bound and frequency weighted generalizations. — Proc. 23rd Conf. Decision and Control, Las Vegas, NV, pp.127–132.
• Feldmann P. and Freund R. (1995): Efficient linear circuit analysis by Padé approximation via the Lanczos process. — IEEE Trans. Comp. Aided Des. Int. Circ. Syst., Vol.14, No.5, pp.639–649.
• Freund R.W. (1993a): The look-ahead Lanczos process for large nonsymmetric matrices and related algorithms, In: Linear Algebra for Large Scale and Real-Time Applications (M.S. Moonen, G.H. Golub, B.L.R. de Moor, Eds.). — Dordrecht: Kluwer, pp.137–163.
• Freund R.W. (1993b): Solution of shifted linear systems by quasi-minimal residual iterations, In: Numerical Linear Algebra (L. Reichel, A. Ruttan, R.S. Varga, Eds.). — Berlin: de Gruyter, pp.101–121.
• Freund R.W. (1999): Reduced-order modeling techniques based on Krylov subspaces and their use in circuit simulation, In: Applied and Computational Control, Signals, and Circuits, Vol. 1 (B.N. Datta, Ed.). — Boston: Birkhäuser, pp.435–498.
• Gallivan K., Grimme E. and van Dooren P. (1994): Asymptotic waveform evaluation via a Lanczos method. — Appl. Math. Lett., Vol.7, No.5, pp.75–80.
• Gallivan K., Grimme E. and van Dooren P. (1996a): A rational Lanczos algorithm for model reduction. — Numer. Algorithms, Vol.12, No.1–2, pp.33–63.
• Gallivan K., Grimme E., Sorensen D. and van Dooren P. (1996b): On some modifications of the Lanczos algorithm and the relation with Padé approximations, In: ICIAM 95 (K. Kirchgässner, O. Mahrenholtz, R. Mennicken, Eds.). — Berlin: Akademie Verlag, pp.87–116.
• Glover K. (1984): All optimal Hankel-norm approximations of linear multivariable systems and their L∞ -error bounds. — Int. J. Contr., Vol.39, No.6, pp.1115–1193.
• Golub G.H. and van Loan C.F. (1996): Matrix Computations, 3rd Ed. — Baltimore, MD: Johns Hopkins University Press.
• Grimme E. (1997): Krylov projection methods for model reduction. — Ph.D. Thesis, University of Illinois at Urbana-Champaign.
• Grimme E.J., Sorensen D.C. and van Dooren P. (1996): Model reduction of state space systems via an implicitly restarted Lanczos-method. — Numer. Algorithms, Vol.12, No.1–2, pp.1–31.
• Li J.R. and White J. (1999): Efficient model reduction of interconnect via approximate system gramians. — Proc. IEEE/ACM Int. Conf. Computer-Aided Design, San Jose, CA, pp.380–383.
• Li J.R., Wang F. and White J. (1999): An efficient Lyapunov equation-based approach for generating reduced-order models of interconnect. — Proc. 36th Design Automation Conf., New Orleans, LA, pp.1–6.
• Lu A. and Wachspress E.L. (1991): Solution of Lyapunov equations by alternating direction implicit iteration. — Comput. Math. Appl., Vol.21, No.9, pp.43–58.
• Marques N., Kamon M., White J. and Silveira L. (1998): A mixed nodal-mesh formulation for efficient extraction and passive reduced-order modeling of 3D interconnects. — Proc. 35th ACM/IEEE Design Automation Confer., San Francisco, CA, pp.297–302.
• Miguel Silveira L., Kamon M., Elfadel I. and White J. (1996): A coordinate-transformed Arnoldi algorithm for generating guaranteed stable reduced-order models of RLC circuits. — Proc. IEEE/ACM Int. Conf. Computer-Aided Design, San Jose, CA, pp.288–294.
• Moore B.C. (1981): Principal component analysis in linear systems: Controllability, observability, and model reduction. — IEEE Trans. Automat. Contr., Vol.26, pp.17–32.
• Odabasioglu A., Celik M. and Pileggi L. (1998): PRIMA: Passive Reduced-order Interconnect Macromodeling Algorithm. — IEEE Trans. Comp. Aided Des. Int. Circ. Syst., Vol.17, No.8, pp.645–654.
• Penzl T. (1999a): Algorithms for model reduction of large dynamical systems. — Tech. Rep., TU Chemnitz.
• Penzl T. (1999b): A cyclic low-rank Smith method for large sparse Lyapunov equations. — SIAM J. Sci. Comput., Vol.21, No.4, pp.1401–1418 (electronic).
• Pernebo L. and Silverman L.M. (1982): Model reduction via balanced state space representations. — IEEE Trans. Automat. Contr., Vol.27, No.2, pp.382–387.
• Safonov M.G. and Chiang R.Y. (1989): A Schur method for balanced-truncation model reduction. — IEEE Trans. Automat. Contr., Vol.34, No.7, pp.729–733.
• Sontag E.D. (1998): Mathematical Control Theory. — New York: Springer-Verlag.
• Tombs M.S. and Postlethwaite I. (1987): Truncated balanced realization of a stable nonminimal state-space system. — Int. J. Contr., Vol.46, No.4, pp.1319–1330.
• Wachspress E.L. (1995): The ADI Model Problem. — Windsor, CA.