Efficient solution of parabolic equations by Krylov approximation methods
SIAM Journal on Scientific and Statistical Computing
PRIMA: passive reduced-order interconnect macromodeling algorithm
ICCAD '97 Proceedings of the 1997 IEEE/ACM international conference on Computer-aided design
Proceedings of the 1998 IEEE/ACM international conference on Computer-aided design
EDTC '95 Proceedings of the 1995 European conference on Design and Test
Efficient linear circuit analysis by Pade approximation via the Lanczos process
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
NORM: compact model order reduction of weakly nonlinear systems
Proceedings of the 40th annual Design Automation Conference
Analog and RF circuit macromodels for system-level analysis
Proceedings of the 40th annual Design Automation Conference
Piecewise polynomial nonlinear model reduction
Proceedings of the 40th annual Design Automation Conference
Direct Nonlinear Order Reduction with Variational Analysis
Proceedings of the conference on Design, automation and test in Europe - Volume 2
A Hybrid Approach to Nonlinear Macromodel Generation for Time-Varying Analog Circuits
Proceedings of the 2003 IEEE/ACM international conference on Computer-aided design
Performance space modeling for hierarchical synthesis of analog integrated circuits
Proceedings of the 42nd annual Design Automation Conference
Parameterized model order reduction of nonlinear dynamical systems
ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
Stabilizing schemes for piecewise-linear reduced order models via projection and weighting functions
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
Bounding L2 gain system error generated by approximations of the nonlinear vector field
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
Numerical Simulation and Modelling of Electronic and Biochemical Systems
Foundations and Trends in Electronic Design Automation
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
A Framework for Reduced Order Modeling with Mixed Moment Matching and Peak Error Objectives
SIAM Journal on Scientific Computing
Nonlinear Model Reduction via Discrete Empirical Interpolation
SIAM Journal on Scientific Computing
Krylov-Based Model Order Reduction of Time-delay Systems
SIAM Journal on Matrix Analysis and Applications
Model order reduction for dynamic simulation of beams with forcing and geometric nonlinearities
Finite Elements in Analysis and Design
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In this paper we present an approach to the nonlinear model reduction based on representing the nonlinear system with a piecewise-linear system and then reducing each of the pieces with a Krylov projection. However, rather than approximating the individual components as piecewise-linear and then composing hundreds of components to make a system with exponentially many different linear regions, we instead generate a small set of linearizations about the state trajectory which is the response to a 'training input'. Computational results and performance data are presented for a nonlinear circuit and a micromachined fixed-fixed beam example. These examples demonstrate that the macromodels obtained with the proposed reduction algorithm are significantly more accurate than models obtained with linear or the recently developed quadratic reduction techniques. Finally, it is shown that the proposed technique is computationally inexpensive, and that the models can be constructed 'on-the-fly', to accelerate simulation of the system response.