Recent Advances in Structure-Preserving Model Order Reduction

In recent years, model order reduction techniques based on Krylov subspaces have become the methods of choice for generating small-scale macromodels of the large-scale multi-port RCL networks that arise in VLSI interconnect analysis. A difficult and not yet completely resolved issue is how to ensure that the resulting macromodels preserve all the relevant structures of the original large-scale RCL networks. In this paper, we present a brief review of how Krylov subspace techniques emerged as the algorithms of choice in VLSI circuit simulation, describe the current state-of-art of structure-preserving model order reduction, discuss some recent advances, and mention open problems.

[1]  W. C. Elmore.  The Transient Response of Damped Linear Networks with Particular Regard to Wideband Amplifiers , 1948 .

[2]  Eric James Grimme,et al.  Krylov Projection Methods for Model Reduction , 1997 .

[3]  Roland W. Freund.  SPRIM: structure-preserving reduced-order interconnect macromodeling , 2004, ICCAD 2004.

[4]  Zhaojun Bai,et al.  How to make theoretically passive reduced-order models passive in practice , 1998, Proceedings of the IEEE 1998 Custom Integrated Circuits Conference (Cat. No.98CH36143).

[5]  Roland W. Freund,et al.  Reduced-Order Modeling of Large Linear Subcircuits via a Block Lanczos Algorithm , 1995, 32nd Design Automation Conference.

[6]  D. Sorensen,et al.  Approximation of large-scale dynamical systems: an overview , 2004 .

[7]  Peter Graves-Morris,et al.  Padé Approximants Second Edition: Contents , 1996 .

[8]  Michel S. Nakhla,et al.  Analysis of interconnect networks using complex frequency hopping (CFH) , 1995, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[9]  P. Feldmann,et al.  The SyMPVL algorithm and its applications to interconnect simulation , 1997, SISPAD '97. 1997 International Conference on Simulation of Semiconductor Processes and Devices. Technical Digest.

[10]  R. Freund.  Krylov-subspace methods for reduced-order modeling in circuit simulation , 2000 .

[11]  Lawrence T. Pileggi,et al.  Asymptotic waveform evaluation for timing analysis , 1990, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[12]  Roland W. Freund,et al.  On Pade-type model order reduction of J-Hermitian linear dynamical systems ⋆ , 2008 .

[13]  Albert E. Ruehli.  Circuit analysis, simulation, and design: general aspects of circuit analysis and design , 1986 .

[14]  Roland W. Freund,et al.  Structure-Preserving Model Order Reduction of RCL Circuit Equations , 2008 .

[15]  Larry Pileggi,et al.  IC Interconnect Analysis , 2002 .

[16]  Lawrence T. Pileggi,et al.  PRIMA: passive reduced-order interconnect macromodeling algorithm , 1997, ICCAD 1997.

[17]  Franklin Fa-Kun Kuo,et al.  Network analysis and synthesis , 1962 .

[18]  Karen Willcox,et al.  Model reduction for active control design using multiple-point Arnoldi methods , 2003 .

[19]  Oliver G. Ernst,et al.  A Restarted Krylov Subspace Method for the Evaluation of Matrix Functions , 2006, SIAM J. Numer. Anal..

[20]  B. Sheehan,et al.  ENOR: model order reduction of RLC circuits using nodal equations for efficient factorization , 1999, Proceedings 1999 Design Automation Conference (Cat. No. 99CH36361).

[21]  Ronald A. Rohrer,et al.  Electronic Circuit and System Simulation Methods , 1994 .

[22]  J. Willems.  Dissipative dynamical systems Part II: Linear systems with quadratic supply rates , 1972 .

[23]  Roland W. Freund,et al.  The SPRIM Algorithm for Structure-Preserving Order Reduction of General RCL Circuits , 2011 .

[24]  Kishore Singhal,et al.  Computer Methods for Circuit Analysis and Design , 1983 .

[25]  Athanasios C. Antoulas,et al.  Approximation of Large-Scale Dynamical Systems , 2005, Advances in Design and Control.

[26]  Lawrence T. Pileggi,et al.  PRIMA: passive reduced-order interconnect macromodeling algorithm , 1998, 1997 Proceedings of IEEE International Conference on Computer Aided Design (ICCAD).

[27]  R. Freund.  Model reduction methods based on Krylov subspaces , 2003, Acta Numerica.

[28]  Robert Skelton,et al.  Model reductions using a projection formulation , 1987, 26th IEEE Conference on Decision and Control.

[29]  Roland W. Freund,et al.  Efficient linear circuit analysis by Pade´ approximation via the Lanczos process , 1994, EURO-DAC '94.

[30]  Roland W. Freund,et al.  Reduced-order modeling of large linear passive multi-terminal circuits using matrix-Pade approximation , 1998, Proceedings Design, Automation and Test in Europe.

[31]  Narsingh Deo,et al.  Graph Theory with Applications to Engineering and Computer Science , 1975, Networks.

[32]  Brian D. O. Anderson,et al.  Network Analysis and Synthesis , 1973 .

[33]  Jacob K. White,et al.  Automatic generation of accurate circuit models of 3-D interconnect , 1998 .

[34]  Louis Weinberg,et al.  Network Analysis and Synthesis , 1962 .