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A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices
- in Proc. Int. Conf. Computer-Aided Design
"... Abstract—In this paper, we present an approach to nonlinear model reduction based on representing a 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 ..."
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Cited by 144 (8 self)
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Abstract—In this paper, we present an approach to nonlinear model reduction based on representing a 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 an example of a micromachined switch and selected nonlinear circuits. These examples demonstrate that the macromodels obtained with the proposed reduction algorithm are significantly more accurate than models obtained with linear or recently developed quadratic reduction techniques. Also, we propose a procedure for a posteriori estimation of the simulation error, which may be used to determine the accuracy of the extracted trajectory piecewise-linear reduced-order models. Finally, it is shown that the proposed model order reduction technique is computationally inexpensive, and that the models can be constructed “on the fly, ” to accelerate simulation of the system response. Index Terms—Microelectromechanical systems (MEMS), model order reduction, nonlinear analog circuits, nonlinear dynamical systems, piecewise-linear models. I.
A multiparameter moment matching model reduction approach for generating geometrically parametrized interconnect performance models
- IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
, 2004
"... this paper we describe an approach for generating geometrically-parameterized integrated-circuit interconnect models that are efficient enough for use in interconnect synthesis. The model generation approach presented is automatic, and is based on a multi-parameter model-reduction algorithm. The eff ..."
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Cited by 97 (8 self)
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this paper we describe an approach for generating geometrically-parameterized integrated-circuit interconnect models that are efficient enough for use in interconnect synthesis. The model generation approach presented is automatic, and is based on a multi-parameter model-reduction algorithm. The effectiveness of the technique is tested using a multi-line bus example, where both wire spacing and wire width are con-sidered as geometric parameters. Experimental results demonstrate that the generated models accurately predict both delay and cross-talk effects over a wide range of spacing and width variation.
A Coordinate-Transformed Arnoldi Algorithm for Generating Guaranteed Stable Reduced-Order Models of RLC Circuits
, 1996
"... Since the first papers on asymptotic waveform evaluation (AWE), Padé-based reduced-order models have become standard for improving coupled circuit-interconnect simulation efficiency. Such models can be accurately computed using bi-orthogonalization algorithms like Padé via Lanczos (PVL), but the res ..."
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Cited by 93 (20 self)
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Since the first papers on asymptotic waveform evaluation (AWE), Padé-based reduced-order models have become standard for improving coupled circuit-interconnect simulation efficiency. Such models can be accurately computed using bi-orthogonalization algorithms like Padé via Lanczos (PVL), but the resulting Padé approximates can still be unstable even when generated from stable RLC circuits. For certain classes of RC circuits it has been shown that congruence transforms, like the Arnoldi algorithm, can generate guaranteed stable and passive reduced-order models. In this paper we present a computationally efficient model-order reduction technique, the coordinate-transformed Arnoldi algorithm, and show that this method generates arbitrarily accurate and guaranteed stable reduced-order models for RLC circuits. Examples are presented which demonstrates the enhanced stability and efficiency of the new method.
Krylov Subspace Techniques for Reduced-Order Modeling of Nonlinear Dynamical Systems
- Appl. Numer. Math
, 2002
"... Means of applying Krylov subspace techniques for adaptively extracting accurate reducedorder models of large-scale nonlinear dynamical systems is a relatively open problem. There has been much current interest in developing such techniques. We focus on a bi-linearization method, which extends Kry ..."
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Cited by 93 (5 self)
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Means of applying Krylov subspace techniques for adaptively extracting accurate reducedorder models of large-scale nonlinear dynamical systems is a relatively open problem. There has been much current interest in developing such techniques. We focus on a bi-linearization method, which extends Krylov subspace techniques for linear systems. In this approach, the nonlinear system is first approximated by a bilinear system through Carleman bilinearization. Then a reduced-order bilinear system is constructed in such a way that it matches certain number of multimoments corresponding to the first few kernels of the Volterra-Wiener representation of the bilinear system. It is shown that the two-sided Krylov subspace technique matches significant more number of multimoments than the corresponding one-side technique.
A collection of benchmark examples for model reduction of linear time invariant dynamical systems. SLICOT Working Note 2002-2. Available from
"... Summary. We present a benchmark collection containing some useful real world examples, which can be used to test and compare numerical methods for model reduction. All systems can be downloaded from the web and we describe here the relevant characteristics of the benchmark examples. 1 ..."
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Cited by 73 (10 self)
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Summary. We present a benchmark collection containing some useful real world examples, which can be used to test and compare numerical methods for model reduction. All systems can be downloaded from the web and we describe here the relevant characteristics of the benchmark examples. 1
Reduced-order modeling techniques based on Krylov subspaces and their use in circuit simulation.
, 1998
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Guaranteed Passive Balancing Transformations for Model Order Reduction
, 2002
"... The major concerns in state-of-the-art model reduction algorithms are: achieving accurate models of sufficiently small size, numerically stable and efficient generation of the models, and preservation of system properties such as passivity. Algorithms such as PRIMA generate guaranteed-passive models ..."
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Cited by 66 (8 self)
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The major concerns in state-of-the-art model reduction algorithms are: achieving accurate models of sufficiently small size, numerically stable and efficient generation of the models, and preservation of system properties such as passivity. Algorithms such as PRIMA generate guaranteed-passive models, for systems with special internal structure, using numerically stable and efficient Krylov-subspace iterations. Truncated Balanced Realization (TBR) algorithms, as used to date in the design automation community, can achieve smaller models with better error control, but do not necessarily preserve passivity. In this paper we show how to construct TBR-like methods that guarantee passive reduced models and in addition are applicable to state-space systems with arbitrary internal structure.
Simulation of High-Speed Interconnects
- PROC. IEEE, MAY 2001
, 2001
"... With the rapid developments in very large-scale integration (VLSI) technology, design and computer-aided design (CAD) techniques, at both the chip and package level, the operating fre-quencies are fast reaching the vicinity of gigahertz and switching times are getting to the subnanosecond levels. Th ..."
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Cited by 61 (3 self)
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With the rapid developments in very large-scale integration (VLSI) technology, design and computer-aided design (CAD) techniques, at both the chip and package level, the operating fre-quencies are fast reaching the vicinity of gigahertz and switching times are getting to the subnanosecond levels. The ever increasing quest for high-speed applications is placing higher demands on interconnect performance and highlighted the previously negligible effects of interconnects, such as ringing, signal delay, distortion, reflections, and crosstalk. In this review paper, various high-speed interconnect effects are briefly discussed. In addition, recent advances in transmission line macromodeling techniques are presented. Also, simulation of high-speed interconnects using model-reduction-based algorithms is discussed in detail.
Krylov-subspace methods for reduced-order modeling in circuit simulation
- Journal of Computational and Applied Mathematics
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