© 2011

Model Reduction for Circuit Simulation

  • Peter Benner
  • Michael Hinze
  • E. Jan W. ter Maten


  • Future direction in MOR for circuit simulations

  • Aspects of MOR related to miniaturization to nano-scale


Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 74)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Invited Papers

  3. Contributed Papers

    1. Front Matter
      Pages 109-109
    2. Luciano De Tommasi, Joost Rommes, Theo Beelen, Marcel Sevat, Jeroen A. Croon, Tom Dhaene
      Pages 111-124
    3. Francesco Ferranti, Dirk Deschrijver, Luc Knockaert, Tom Dhaene
      Pages 141-148
    4. Mark M. Gourary, Sergey G. Rusakov, Sergey L. Ulyanov, Michael M. Zharov
      Pages 149-161
    5. Michael Hinze, Martin Kunkel, Morten Vierling
      Pages 177-192
    6. Peter Benner, Mohammad-Sahadet Hossain, Tatjana Stykel
      Pages 193-206
    7. Roxana Ionutiu, Joost Rommes
      Pages 207-223
    8. Rostylav V. Polyuga, Arjan J. van der Schaft
      Pages 241-260
    9. Oliver Schmidt, Thomas Halfmann, Patrick Lang
      Pages 261-275
    10. Peter Benner, André Schneider
      Pages 277-288

About this book


Simulation based on mathematical models plays a major role in computer aided design of integrated circuits (ICs). Decreasing structure sizes, increasing packing densities and driving frequencies require the use of refined mathematical models, and to take into account secondary, parasitic effects. This leads to very high dimensional problems which nowadays require simulation times too large for the short time-to-market demands in industry. Modern Model Order Reduction (MOR) techniques present a way out of this dilemma in providing surrogate models which keep the main characteristics of the device while requiring a significantly lower simulation time than the full model.

With Model Reduction for Circuit Simulation we survey the state of the art in the challenging research field of MOR for ICs, and also address its future research directions. Special emphasis is taken on aspects stemming from miniturisations to the nano scale. Contributions cover complexity reduction using e.g., balanced truncation, Krylov-techniques or POD approaches. For semiconductor applications a focus is on generalising current techniques to differential-algebraic equations, on including design parameters, on preserving stability, and on including nonlinearity by means of piecewise linearisations along solution trajectories (TPWL) and interpolation techniques for nonlinear parts. Furthermore the influence of interconnects and power grids on the physical properties of the device is considered, and also top-down system design approaches in which detailed block descriptions are combined with behavioral models. Further topics consider MOR and the combination of approaches from optimisation and statistics, and the inclusion of PDE models with emphasis on MOR for the resulting partial differential algebraic systems. The methods which currently are being developed have also relevance in other application areas such as mechanical multibody systems, and systems arising in chemistry and to biology.

The current number of books in the area of MOR for ICs is very limited, so that this volume helps to fill a gap in providing the state of the art material, and to stimulate further research in this area of MOR. Model Reduction for Circuit Simulation also reflects and documents the vivid interaction between three active research projects in this area, namely the EU-Marie Curie Action ToK project O-MOORE-NICE (members in Belgium, The Netherlands and Germany), the EU-Marie Curie Action RTN-project COMSON (members in The Netherlands, Italy, Germany, and Romania), and the German federal project System reduction in nano-electronics (SyreNe).


Krylov subspace methods Models-Order-Reduction (MOR) integrated circuit design model order reduction nanotechnology proper orthogonal decomposition

Editors and affiliations

  • Peter Benner
    • 1
  • Michael Hinze
    • 2
  • E. Jan W. ter Maten
    • 3
  1. 1.Inst. Dynamics of Complex Techn. SystemsMax Planck InstituteMagdeburgGermany
  2. 2., Fachbereich MathematikUniversität HamburgHamburgGermany
  3. 3., Dept. Mathematics & Comp. Sci.Eindhoven University of TechnologyEindhovenNetherlands

Bibliographic information

  • Book Title Model Reduction for Circuit Simulation
  • Editors Peter Benner
    Michael Hinze
    E. Jan W. ter Maten
  • Series Title Lecture Notes in Electrical Engineering
  • DOI
  • Copyright Information Springer Science+Business Media B.V. 2011
  • Publisher Name Springer, Dordrecht
  • eBook Packages Engineering Engineering (R0)
  • Hardcover ISBN 978-94-007-0088-8
  • Softcover ISBN 978-94-007-3283-4
  • eBook ISBN 978-94-007-0089-5
  • Series ISSN 1876-1100
  • Series E-ISSN 1876-1119
  • Edition Number 1
  • Number of Pages XIII, 315
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Circuits and Systems
    Mathematical and Computational Engineering
    Systems Theory, Control
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