Projection frameworks for model reduction of weakly nonlinear systems
Proceedings of the 37th Annual Design Automation Conference
Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems
Applied Numerical Mathematics
Proceedings of the 40th annual Design Automation Conference
Automated nonlinear Macromodelling of output buffers for high-speed digital applications
Proceedings of the 42nd annual Design Automation Conference
Scalable trajectory methods for on-demand analog macromodel extraction
Proceedings of the 42nd annual Design Automation Conference
Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control)
SPRIM: structure-preserving reduced-order interconnect macromodeling
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
Parameterized model order reduction of nonlinear dynamical systems
ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
Faster, parametric trajectory-based macromodels via localized linear reductions
Proceedings of the 2006 IEEE/ACM international conference on Computer-aided design
Linearized reduced-order models for subsurface flow simulation
Journal of Computational Physics
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Automated compact dynamical modeling: an enabling tool for analog designers
Proceedings of the 47th Design Automation Conference
Nonlinear Model Reduction via Discrete Empirical Interpolation
SIAM Journal on Scientific Computing
Original article: Machine tool simulation based on reduced order FE models
Mathematics and Computers in Simulation
Structure-preserving model reduction
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
PRIMA: passive reduced-order interconnect macromodeling algorithm
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Asymptotic waveform evaluation for timing analysis
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
General-Purpose Nonlinear Model-Order Reduction Using Piecewise-Polynomial Representations
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Efficient linear circuit analysis by Pade approximation via the Lanczos process
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Mathematics and Computers in Simulation
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Trajectory based methods approximate nonlinear dynamical systems by superposition of dimensionally reduced linear systems. The linear systems are obtained by linearisations at multiple points along a state-trajectory. They are combined in a weighted sum and the combinations are switched appropriately to approximate the dynamic behaviour of the nonlinear system. Weights assigned at a specimen point on the trajectory generally depend on the euclidean distance to the linearisation points. In this work, limitations of the conventional weight-assignment scheme are pointed out. It is shown that the procedure is similar across all nonlinearities, and hence ignores the nonlinear vector field curvature for superposition. Additionally, it results in an inadequate assessment of the linear systems when they are equidistant from the specimen point. An improved method for weight-assignment, which uses state-velocities in addition to state-positions is proposed. The method naturally takes into account the system nonlinearity and is hence called Nonlinearity-aware Trajectory Piece-wise Linear (Ntpwl) method. Further, a computationally efficient procedure for estimating the state-velocity is introduced. The new strategy is illustrated and assessed with the help of case studies and it is shown that the Ntpwl model substantially improves the approximation of the nonlinear systems considered. Increased robustness to training and negligible stretching of the computational resources is also obtained.