Nonlinear systems analysis (2nd ed.)
Nonlinear systems analysis (2nd ed.)
Efficient linear circuit analysis by Pade´ approximation via the Lanczos process
EURO-DAC '94 Proceedings of the conference on European design automation
Stable and efficient reduction of substrate model networks using congruence transforms
ICCAD '95 Proceedings of the 1995 IEEE/ACM international conference on Computer-aided design
Krylov-subspace methods for reduced-order modeling in circuit simulation
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Poor Man's TBR: A Simple Model Reduction Scheme
Proceedings of the conference on Design, automation and test in Europe - Volume 2
pFFT in FastMaxwell: a fast impedance extraction solver for 3D conductor structures over substrate
Proceedings of the conference on Design, automation and test in Europe
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
PRIMA: passive reduced-order interconnect macromodeling algorithm
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Guaranteed passive balancing transformations for model order reduction
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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
Proceedings of the 16th Asia and South Pacific Design Automation Conference
Proceedings of the 48th Design Automation Conference
Enhanced linearized reduced-order models for subsurface flow simulation
Journal of Computational Physics
Reliable reduced-order models for time-dependent linearized Euler equations
Journal of Computational Physics
Journal of Electronic Testing: Theory and Applications
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In this work we present a stability-preserving projection framework for model reduction of linear systems. Specifically, given one projection matrix (e.g. a right-projection matrix), we derive a set of linear constraints for the other projection matrix (e.g. the left-projection matrix) resulting in a projection framework that is guaranteed to generate a stable reduced model. Several efficient techniques for solving the proposed system of constraints are presented, including an optimization problem formulation for finding the optimal stabilizing projection, and a formulation with computational complexity independent of the size of the original system. The resulting algorithms can create accurate stable and passive models of arbitrary indefinite systems at a significantly cheaper cost than existing methods such as balanced truncation. Nevertheless, our algorithms integrate fully and effortlessly with most of the available standard model order reduction approaches for very large systems generated in VLSI applications (such as moment-matching methods, POD, or Poor Man's TBR), which can guarantee stability and passivity only in very specialized cases. Our algorithms have been tested on a large variety of typical VLSI applications, including field-solver-extracted models of RF inductors for analog applications, power distribution grids for large VLSI digital integrated circuits, and MEMS devices for sensing and actuation applications. The results have been successfully compared to those from existing and much more expensive stabilizing reduction techniques.