Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
MTZ-Fachkongress

Antriebe und Energiesysteme von morgen


Austausch von Automobil- und Energiewirtschaft

Am 14./15. Mai geht es in Chemnitz um die Mobilitätswende durch Elektro- und Wasserstofffahrzeuge.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Model Order Reduction of Integrated Circuits in Electrical Networks Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

2. Element-Based Model Reduction in Circuit Simulation

verfasst von : Andreas Steinbrecher, Tatjana Stykel

Erschienen in: System Reduction for Nanoscale IC Design

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this paper, we consider model reduction of linear and nonlinear differential-algebraic equations arising in circuit simulation. Circuit equations obtained using modified nodal or loop analysis have a ;special structure that can be exploited to construct efficient model reduction algorithms. For linear systems, we review passivity-preserving balanced truncation model reduction methods that are based on solving projected Lur’e or Lyapunov matrix equations. Furthermore, a ;topology-based index-preserving procedure for extracting large linear subnetworks from nonlinear circuits is given. Finally, we describe a ;new MATLAB Toolbox PABTEC for model reduction of circuit equations and present some results of numerical experiments.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Model Order Reduction of Integrated Circuits in Electrical Networks
Nächstes Kapitel Reduced Representation of Power Grid Models
Fußnoten
Literatur
1.
Anderson, B., Vongpanitlerd, S.: Network Analysis and Synthesis. Prentice Hall, Englewood Cliffs, NJ (1973)
2.
Andrásfai, B.: Graph Theory: Flows, Matrices. Adam Hilger, New York/Bristol (1991)MATH
3.
Antoulas, A.: Approximation of Large-Scale Dynamical Systems. SIAM, Philadelphia, PA (2005)CrossRefMATH
4.
5.
Antoulas, A., Beattie, C., Gugercin, S.: Interpolatory model reduction of large-scale dynamical systems. In: Mohammadpour, J., Grigoriadis, K. (eds.) Efficient Modeling and Control of Large-Scale Systems, pp. 3–58. Springer, New York (2010)CrossRef
6.
Bai, Z.: Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems. Appl. Numer. Math. 43, 9–44 (2002)MathSciNetCrossRefMATH
7.
Bechtold, T., Verhoeven, A., ter Maten, E., Voss, T.: Model order reduction: an advanced, efficient and automated computational tool for microsystems. In: Cutello, V., Fotia, G., Puccio, L. (eds.) Applied and Industrial Mathematics in Italy II, Selected Contributions from the 8th SIMAI Conference. Advances in Mathematics for Applied Sciences, vol. 75, pp. 113–124. World Scientific, Singapore (2007)
8.
Benner, P.: Numerical solution of special algebraic Riccati equations via exact line search method. In: Proceedings of the European Control Conference (ECC97), paper 786. BELWARE Information Technology, Waterloo (1997)
9.
Benner, P., Quintana-Ortí, E.: Solving stable generalized Lyapunov equations with the matrix sign function. Numer. Algorithms 20(1), 75–100 (1999)MathSciNetCrossRefMATH
10.
Benner, P., Stykel, T.: Numerical solution of projected algebraic Riccati equations. SIAM J. Numer. Anal. 52(2), 581–600 (2014)MathSciNetCrossRefMATH
11.
Benner, P., Quintana-Ortí, E., Quintana-Ortí, G.: Efficient numerical algorithms for balanced stochastic truncation. Int. J. Appl. Math. Comput. Sci. 11(5), 1123–1150 (2001)MathSciNetMATH
12.
Benner, P., Hernández, V., Pastor, A.: The Kleinman iteration for nonstabilizable systems. Math. Control Signals Syst. 16, 76–93 (2003)MathSciNetMATH
13.
Benner, P., Mehrmann, V., Sorensen, D. (eds.): Dimension Reduction of Large-Scale Systems. Lecture Notes in Computational Science and Engineering, vol. 45. Springer, Berlin/Heidelberg (2005)
14.
Benner, P., Li, J.R., Penzl, T.: Numerical solution of large Lyapunov equations, Riccati equations, and linear-quadratic control problems. Numer. Linear Algebra Appl. 15, 755–777 (2008)MathSciNetCrossRefMATH
15.
Benner, P., Mena, H., Saak, J.: On the parameter selection problem in the Newton-ADI iteration for large-scale Riccati equations. Electron. Trans. Numer. Anal. 29, 136–149 (2008)MathSciNetMATH
16.
Benner, P., Kürschner, P., Saak, J.: Efficient handling of complex shift parameters in the low-rank Cholesky factor ADI method. Numer. Algorithms 62(2), 225–251 (2013)MathSciNetCrossRefMATH
17.
Brenan, K., Campbell, S., Petzold, L.: The Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. Classics in Applied Mathematics, vol. 14. SIAM, Philadelphia, PA (1996)
18.
Chan, T.: Rank revealing QR factorizations. Linear Algebra Appl. 88/89, 67–82 (1987)
19.
20.
Chua, L., Desoer, C., Kuh, E.: Linear and Nonlinear Circuits. McGraw-Hill, New York (1987)MATH
21.
Dai, L.: Singular Control Systems. Lecture Notes in Control and Information Sciences, vol. 118. Springer, Berlin/Heidelberg (1989)
22.
Deo, N.: Graph Theory with Application to Engineering and Computer Science. Prentice-Hall, Englewood Cliffs, NJ (1974)MATH
23.
EstévezSchwarz, D.: A step-by-step approach to compute a consistent initialization for the MNA. Int. J. Circuit Theory Appl. 30, 1–16 (2002)CrossRef
24.
Estévez Schwarz, D., Tischendorf, C.: Structural analysis for electric circuits and consequences for MNA. Int. J. Circuit Theory Appl. 28, 131–162 (2000)CrossRefMATH
25.
26.
Freund, R.: SPRIM: structure-preserving reduced-order interconnect macromodeling. In: Technical Digest of the 2004 IEEE/ACM International Conference on Computer-Aided Design, pp. 80–87. IEEE Computer Society, Los Alamos, CA (2004)
27.
Freund, R.: Structure-preserving model order reduction of RCL circuit equations. In: Schilders, W., van der Vorst, H., Rommes, J. (eds.) Model Order Reduction: Theory, Research Aspects and Applications. Mathematics in Industry, vol. 13, pp. 49–73. Springer, Berlin/Heidelberg (2008)CrossRef
28.
Golub, G., Van Loan, C.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore/London (1996)MATH
29.
Griepentrog, E., März, R.: Differential-Algebraic Equations and Their Numerical Treatment. Teubner-Texte zur Mathematik, vol. 88. B.G. Teubner, Leipzig (1986)
30.
Grimme, E.: Krylov projection methods for model reduction. Ph.D. thesis, University of Illinois, Urbana-Champaign (1997)
31.
Gugercin, S., Antoulas, A.: A survey of model reduction by balanced truncation and some new results. Int. J. Control 77(8), 748–766 (2004)MathSciNetCrossRefMATH
32.
Gugercin, S., Antoulas, A., Beattie, C.: \(\mathcal{H}_{2}\) model reduction for large-scale linear dynamical systems. SIAM J. Matrix Anal. Appl. 30(2), 609–638 (2008)
33.
Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II - Stiff and Differential-Algebraic Problems, 2nd edn. Springer, Berlin (1996)CrossRefMATH
34.
35.
Hinze, M., Kunkel, M.: Residual based sampling in pod model order reduction of drift-diffusion equations in parametrized electrical networks. Z. Angew. Math. Mech. 92(2), 91–104 (2012)MathSciNetCrossRefMATH
36.
Hinze, M., Kunkel, M., Steinbrecher, A., Stykel, T.: Model order reduction of coupled circuit-device systems. Int. J. Numer. Model. Electron. Networks Devices Fields 25, 362–377 (2012)CrossRef
37.
Ho, C.W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Trans. Circuits Syst. 22(6), 504–509 (1975)CrossRef
38.
Ionutiu, R., Rommes, J., Antoulas, A.: Passivity-preserving model reduction using dominant spectral-zero interpolation. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 27(12), 2250–2263 (2008)CrossRef
39.
Ipach, H.: Graphentheoretische Anwendungen in der Analyse elektrischer Schaltkreise. Bachelorarbeit, Universität Hamburg (2013)
40.
Jungnickel, D.: Graphs, Network and Algorithms. Springer, Berlin/Heidelberg (2005)MATH
41.
Kleinman, D.: On an iterative technique for Riccati equation computations. IEEE Trans. Autom. Control 13, 114–115 (1968)CrossRef
42.
Knockaert, L., De Zutter, D.: Laguerre-SVD reduced-order modeling. IEEE Trans. Microwave Theory Tech. 48(9), 1469–1475 (2000)CrossRef
43.
Kunkel, P., Mehrmann, V.: Differential-Algebraic Equations. Analysis and Numerical Solution. EMS Publishing House, Zürich (2006)CrossRefMATH
44.
45.
Liu, W., Sreeram, V., Teo, K.: Model reduction for state-space symmetric systems. Syst. Control Lett. 34(4), 209–215 (1998)MathSciNetCrossRefMATH
46.
Moore, B.: Principal component analysis in linear systems: controllability, observability, and model reduction. IEEE Trans. Autom. Control 26(1), 17–32 (1981)MathSciNetCrossRefMATH
47.
48.
Odabasioglu, A., Celik, M., Pileggi, L.: PRIMA: passive reduced-order interconnect macromodeling algorithm. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 17(8), 645–654 (1998)CrossRef
49.
Ovalekar, V., Narayanan, H.: Fast loop matrix generation for hybrid analysis and a comparison of the sparsity of the loop impedance and MNA impedance submatrices. In: Proceedings of the IEEE International Symposium on Circuits and Systems, ISCAS ’92, vol. 4, pp. 1780–1783 (1992)
50.
Penzl, T.: A cyclic low-rank Smith method for large sparse Lyapunov equations. SIAM J. Sci. Comput. 21(4), 1401–1418 (1999/2000)
51.
52.
Phillips, J., Daniel, L., Silveira, L.: Guaranteed passive balancing transformations for model order reduction. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 22(8), 1027–1041 (2003)CrossRef
53.
Poloni, F., Reis, T.: A deflation approach for large-scale Lur’e equations. SIAM. J. Matrix Anal. Appl. 33(4), 1339–1368 (2012)MathSciNetCrossRefMATH
54.
Reis, T., Stykel, T.: PABTEC: Passivity-preserving balanced truncation for electrical circuits. IEEE Trans. Compu. Aided Des. Integr. Circuits Syst. 29(9), 1354–1367 (2010)CrossRef
55.
Reis, T., Stykel, T.: Positive real and bounded real balancing for model reduction of descriptor systems. Int. J. Control 83(1), 74–88 (2010)MathSciNetCrossRefMATH
56.
Reis, T., Stykel, T.: Lyapunov balancing for passivity-preserving model reduction of RC circuits. SIAM J. Appl. Dyn. Syst. 10(1), 1–34 (2011)MathSciNetCrossRefMATH
57.
Rewieński, M.: A trajectory piecewise-linear approach to model order reduction of nonlinear dynamical systems. Ph.D. thesis, Massachusetts Institute of Technology (2003)
58.
Riaza, R., Tischendorf, C.: Qualitative features of matrix pencils and DAEs arising in circuit dynamics. Dyn. Syst. 22, 107–131 (2007)MathSciNetCrossRefMATH
59.
Riaza, R., Tischendorf, C.: The hyperbolicity problem in electrical circuit theory. Math. Methods Appl. Sci. 33(17), 2037–2049 (2010)MathSciNetCrossRefMATH
60.
Rommes, J., Schilders, W.: Efficient methods for large resistor networks. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 29(1), 28–39 (2010)CrossRef
61.
Roos, J., Costa, L. (eds.): Scientific Computing in Electrical Engineering SCEE 2008. Mathematics in Industry, vol. 14. Springer, Berlin/Heidelberg (2010)
62.
Saad, Y.: Iterative Methods for Sparse Linear Systems. PWS Publishing Company, Boston, MA (1996)MATH
63.
Sabino, J.: Solution of large-scale Lyapunov equations via the block modified Smith method. Ph.D. thesis, Rice University, Houston (2006)
64.
Schilders, W., van der Vorst, H., J., R. (eds.): Model Order Reduction: Theory, Research Aspects and Applications. Mathematics in Industry, vol. 13. Springer, Berlin/Heidelberg (2008)
65.
Sirovich, L.: Turbulence and the dynamics of coherent structures. I: coherent structures. II: symmetries and transformations. III: dynamics and scaling. Q. Appl. Math. 45, 561–590 (1987)MathSciNetMATH
66.
Sorensen, D.: Passivity preserving model reduction via interpolation of spectral zeros. Syst. Control Lett. 54(4), 347–360 (2005)MathSciNetCrossRefMATH
67.
Soto, M.S., Tischendorf, C.: Numerical analysis of DAEs from coupled circuit and semiconductor simulation. Appl. Numer. Math. 53(2–4), 471–88 (2005)MathSciNetCrossRefMATH
68.
Steinbrecher, A., Stykel, T.: Model order reduction of nonlinear circuit equations. Int. J. Circuits Theory Appl. 41, 1226–1247 (2013)CrossRef
69.
70.
Stykel, T.: Low-rank iterative methods for projected generalized Lyapunov equations. Electron. Trans. Numer. Anal. 30, 187–202 (2008)MathSciNetMATH
71.
Stykel, T.: Balancing-related model reduction of circuit equations using topological structure. In: Benner, P., Hinze, M., ter Maten, E. (eds.) Model Reduction for Circuit Simulation. Lecture Notes in Electrical Engineering, vol. 74, pp. 53–80. Springer, Berlin/Heidelberg (2011)CrossRef
72.
Stykel, T., Reis, T.: The PABTEC algorithm for passivity-preserving model reduction of circuit equations. In: Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010, Budapest, 5–9 July 2010, paper 363. ELTE, Budapest (2010)
73.
Tischendorf, C.: Coupled systems of differential algebraic and partial differential equations in circuit and device simulation. Habilitation thesis, Humboldt-Universität Berlin (2004)
74.
Varga, A.: On computing high accuracy solutions of a class of Riccati equations. Control Theory Adv. Technol. 10, 2005–2016 (1995)MathSciNet
75.
Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Van Nostrand Reinhold, New York (1994)
76.
77.
Wachspress, E.: The ADI minimax problem for complex spectra. In: Kincaid, D., Hayes, L. (eds.) Iterative Methods for Large Linear Systems, pp. 251–271. Academic, San Diego (1990)CrossRef
78.
Wachspress, E.: The ADI Model Problem. Monograph, Windsor, CA (1995)MATH
79.
Weinbreg, L., Ruehili, A.: Combined modified loop analysis, modified nodal analysis for large-scale circuits. IBM Research Report RC 10407, IBM Research Devision (1984)
Metadaten
Titel
Element-Based Model Reduction in Circuit Simulation
verfasst von
Andreas Steinbrecher
Tatjana Stykel
Copyright-Jahr
2017
Buch
System Reduction for Nanoscale IC Design

Print ISBN: 978-3-319-07235-7

Electronic ISBN: 978-3-319-07236-4

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-07236-4_2

Premium Partner

    Bildnachweise