Nonlinear model order reduction based on trajectory piecewise linear approach: Comparing different linear cores

Refined models for MOS-devices and increasing complexity of circuit designs cause the need for Model Order Reduction (MOR) techniques that are capable of treating nonlinear problems. In time-domain simulation the Trajectory PieceWise Linear (TPWL) approach is promising as it is designed to use MOR methodologies for linear problems as the core of the reduction process. We compare different linear approaches with respect to their performance when used as kernel for TPWL.

[1]  Kenji Fujimoto,et al.  Model Reduction of Nonlinear Differential-Algebraic Equations , 2007 .

[2]  Danny C. Sorensen Passivity preserving model reduction via interpolation of spectral zeros , 2003, ECC.

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

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

[5]  Michal Rewienski,et al.  A trajectory piecewise-linear approach to model order reduction of nonlinear dynamical systems , 2003 .

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

[7]  Thomas Voss,et al.  Model Reduction for Nonlinear Differential-Algebraic Equations , 2007 .

[8]  RewieÅ ski,et al.  A trajectory piecewise-linear approach to model order reduction of nonlinear dynamical systems , 2003 .

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

[10]  Luís Miguel Silveira,et al.  Poor man's TBR: a simple model reduction scheme , 2004, Proceedings Design, Automation and Test in Europe Conference and Exhibition.

[11]  E. Grimme,et al.  Pade approximation of large-scale dynamic systems with Lanczos methods , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[12]  Jacob K. White,et al.  An Arnoldi approach for generation of reduced-order models for turbomachinery , 2000 .

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

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

[15]  Danny C. Sorensen,et al.  Passivity preserving model reduction via interpolation of spectral zeros , 2003, 2003 European Control Conference (ECC).

[16]  Roland W. Freund,et al.  SPRIM: structure-preserving reduced-order interconnect macromodeling , 2004, IEEE/ACM International Conference on Computer Aided Design, 2004. ICCAD-2004..

[17]  E. J. W. ter Maten,et al.  Trajectory piecewise linear approach for nonlinear differential-algebraic equations in circuit simulation , 2007 .

[18]  P. Dooren,et al.  Asymptotic Waveform Evaluation via a Lanczos Method , 1994 .