Results 1  10
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70
PRIMA: Passive Reducedorder Interconnect Macromodeling Algorithm
, 1997
"... This paper describes PRIMA, an algorithm for generating provably passive reduced order Nport models for RLC interconnect circuits. It is demonstrated that, in addition to requiring macromodel stability, macromodel passivity is needed to guarantee the overall circuit stability once the active and pa ..."
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Cited by 429 (10 self)
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This paper describes PRIMA, an algorithm for generating provably passive reduced order Nport models for RLC interconnect circuits. It is demonstrated that, in addition to requiring macromodel stability, macromodel passivity is needed to guarantee the overall circuit stability once the active and passive driver/load models are connected. PRIMA extends the block Arnoldi technique to include guaranteed passivity. Moreover, it is empirically observed that the accuracy is superior to existing block Arnoldi methods. While the same passivity extension is not possible for MPVL, we observed comparable accuracy in the frequency domain for all examples considered. Additionally, a path tracing algorithm is used to calculate the reduced order macromodel with the utmost efficiency for generalized RLC interconnects.
Extracting macroscopic dynamics: model problems and algorithms
 NONLINEARITY
, 2004
"... In many applications, the primary objective of numerical simulation of timeevolving systems is the prediction of macroscopic, or coarsegrained, quantities. A representative example is the prediction of biomolecular conformations from molecular dynamics. In recent years a number of new algorithmic ..."
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Cited by 111 (8 self)
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In many applications, the primary objective of numerical simulation of timeevolving systems is the prediction of macroscopic, or coarsegrained, quantities. A representative example is the prediction of biomolecular conformations from molecular dynamics. In recent years a number of new algorithmic approaches have been introduced to extract effective, lowerdimensional, models for the macroscopic dynamics; the starting point is the full, detailed, evolution equations. In many cases the effective lowdimensional dynamics may be stochastic, even when the original starting point is deterministic. This review surveys a number of these new approaches to the problem of extracting effective dynamics, highlighting similarities and differences between them. The importance of model problems for the evaluation of these new approaches is stressed, and a number of model problems are described. When the macroscopic dynamics is stochastic, these model problems are either obtained through a clear separation of timescales, leading to a stochastic effect of the fast dynamics on the slow dynamics, or by considering high dimensional ordinary differential equations which, when projected onto a low dimensional subspace, exhibit stochastic behaviour through the presence of a broad frequency spectrum. Models whose stochastic microscopic behaviour leads to deterministic macroscopic dynamics are also introduced. The algorithms we overview include SVDbased methods for nonlinear problems, model reduction for linear control systems, optimal prediction techniques, asymptoticsbased mode elimination, coarse timestepping methods and transferoperator based methodologies.
Krylov Subspace Techniques for ReducedOrder Modeling of Nonlinear Dynamical Systems
 Appl. Numer. Math
, 2002
"... Means of applying Krylov subspace techniques for adaptively extracting accurate reducedorder models of largescale nonlinear dynamical systems is a relatively open problem. There has been much current interest in developing such techniques. We focus on a bilinearization 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 largescale nonlinear dynamical systems is a relatively open problem. There has been much current interest in developing such techniques. We focus on a bilinearization 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 reducedorder bilinear system is constructed in such a way that it matches certain number of multimoments corresponding to the first few kernels of the VolterraWiener representation of the bilinear system. It is shown that the twosided Krylov subspace technique matches significant more number of multimoments than the corresponding oneside technique.
Approximation of largescale dynamical systems: An overview
, 2001
"... In this paper we review the state of affairs in the area of approximation of largescale systems. We distinguish among three basic categories, namely the SVDbased, the Krylovbased and the SVDKrylovbased approximation methods. The first two were developed independently of each other and have dist ..."
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Cited by 71 (3 self)
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In this paper we review the state of affairs in the area of approximation of largescale systems. We distinguish among three basic categories, namely the SVDbased, the Krylovbased and the SVDKrylovbased approximation methods. The first two were developed independently of each other and have distinct sets of attributes and drawbacks. The third approach seeks to combine the best attributes of the first two. Contents 1 Introduction and problem statement 1 2 Motivating Examples 3 3 Approximation methods 4 3.1 SVDbased approximation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.1.1 The Singular value decomposition: SVD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.1.2 Proper Orthogonal Decomposition (POD) methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.1.3 Approximation by balanced truncation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
Simulation of HighSpeed Interconnects
 PROC. IEEE, MAY 2001
, 2001
"... With the rapid developments in very largescale integration (VLSI) technology, design and computeraided design (CAD) techniques, at both the chip and package level, the operating frequencies 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 largescale integration (VLSI) technology, design and computeraided design (CAD) techniques, at both the chip and package level, the operating frequencies are fast reaching the vicinity of gigahertz and switching times are getting to the subnanosecond levels. The ever increasing quest for highspeed 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 highspeed interconnect effects are briefly discussed. In addition, recent advances in transmission line macromodeling techniques are presented. Also, simulation of highspeed interconnects using modelreductionbased algorithms is discussed in detail.
Krylovsubspace methods for reducedorder modeling in circuit simulation
 Journal of Computational and Applied Mathematics
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Solving LargeScale Control Problems
, 2004
"... Sparsity and parallel algorithms: two approaches to beat the curse of dimensionality. By Peter Benner I n this article we discuss sparse matrix algorithms and parallel algorithms, as well as their application to largescale systems. For illustration, we solve the linearquadratic regulator (LQR) pro ..."
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Cited by 54 (26 self)
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Sparsity and parallel algorithms: two approaches to beat the curse of dimensionality. By Peter Benner I n this article we discuss sparse matrix algorithms and parallel algorithms, as well as their application to largescale systems. For illustration, we solve the linearquadratic regulator (LQR) problem and apply balanced truncation model reduction using either parallel computing or sparse matrix algorithms. We conclude that modern tools from numerical linear algebra, along with careful investigation and exploitation of the problem structure, can be used to derive algorithms capable of solving large control problems. Since these approaches are implemented in productionquality software, control engineers can employ complex models and use computational tools to analyze and design feedback control laws. Background
Algorithms for Model Reduction of Large Dynamical Systems
, 1999
"... Three algorithms for the model reduction of largescale, continuoustime, timeinvariant, linear, dynamical systems with a sparse or structured transition matrix and a small number of inputs and outputs are described. They rely on low rank approximations to the controllability and observability Gram ..."
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Cited by 53 (1 self)
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Three algorithms for the model reduction of largescale, continuoustime, timeinvariant, linear, dynamical systems with a sparse or structured transition matrix and a small number of inputs and outputs are described. They rely on low rank approximations to the controllability and observability Gramians, which can eciently be computed by ADI based iterative low rank methods. The rst two model reduction methods are closely related to the wellknown square root method and Schur method, which are balanced truncation techniques. The third method is a heuristic, balancingfree technique. The performance of the model reduction algorithms is studied in numerical experiments.
Reducedorder modeling of timevarying systems
 Circuits and Systems II: Analog and Digital Signal Processing
, 1999
"... We present a theory for reducedorder modelling of linear timevarying systems, together with efficient numerical methods for application to large systems. The technique, called TVP (TimeVarying Padk), is applicable to deterministic as well as noise analysis of many types of communication subsystem ..."
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Cited by 47 (9 self)
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We present a theory for reducedorder modelling of linear timevarying systems, together with efficient numerical methods for application to large systems. The technique, called TVP (TimeVarying Padk), is applicable to deterministic as well as noise analysis of many types of communication subsystems, such as mixers and switchedcapacitor filters, for which existing model reduction techniques cannot be used. TVP is therefore suitable for hierarchical verification of entire communication systems. We present practical applications in which TVP generates macromodels which are more than two orders of magnitude smaller, but still replicate the inputoutput behaviour of the original systems accurately. The size reduction results in a speedup of more than 500. 1