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45
Krylov Projection Methods For Model Reduction
, 1997
"... This dissertation focuses on efficiently forming reducedorder models for large, linear dynamic systems. Projections onto unions of Krylov subspaces lead to a class of reducedorder models known as rational interpolants. The cornerstone of this dissertation is a collection of theory relating Krylov p ..."
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Cited by 149 (3 self)
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This dissertation focuses on efficiently forming reducedorder models for large, linear dynamic systems. Projections onto unions of Krylov subspaces lead to a class of reducedorder models known as rational interpolants. The cornerstone of this dissertation is a collection of theory relating Krylov projection to rational interpolation. Based on this theoretical framework, three algorithms for model reduction are proposed. The first algorithm, dual rational Arnoldi, is a numerically reliable approach involving orthogonal projection matrices. The second, rational Lanczos, is an efficient generalization of existing Lanczosbased methods. The third, rational power Krylov, avoids orthogonalization and is suited for parallel or approximate computations. The performance of the three algorithms is compared via a combination of theory and examples. Independent of the precise algorithm, a host of supporting tools are also developed to form a complete modelreduction package. Techniques for choosing the matching frequencies, estimating the modeling error, insuring the model's stability, treating multipleinput multipleoutput systems, implementing parallelism, and avoiding a need for exact factors of large matrix pencils are all examined to various degrees.
A CoordinateTransformed Arnoldi Algorithm for Generating Guaranteed Stable ReducedOrder Models of RLC Circuits
, 1996
"... Since the first papers on asymptotic waveform evaluation (AWE), Padébased reducedorder models have become standard for improving coupled circuitinterconnect simulation efficiency. Such models can be accurately computed using biorthogonalization algorithms like Padé via Lanczos (PVL), but the res ..."
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Cited by 72 (14 self)
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Since the first papers on asymptotic waveform evaluation (AWE), Padébased reducedorder models have become standard for improving coupled circuitinterconnect simulation efficiency. Such models can be accurately computed using biorthogonalization 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 reducedorder models. In this paper we present a computationally efficient modelorder reduction technique, the coordinatetransformed Arnoldi algorithm, and show that this method generates arbitrarily accurate and guaranteed stable reducedorder models for RLC circuits. Examples are presented which demonstrates the enhanced stability and efficiency of the new method.
Interconnect design for deep submicron ICs
 IN PROC. INT. CONF. ON COMPUTER AIDED DESIGN
, 1997
"... Interconnect has become the dominating factor in determining circuit performance and reliability in deep submicron designs. In this embedded tutorial, we first discuss the trends and challenges of interconnect design as the technology feature size rapidly decreases towards below 0.1 micron. Then, we ..."
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Cited by 72 (22 self)
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Interconnect has become the dominating factor in determining circuit performance and reliability in deep submicron designs. In this embedded tutorial, we first discuss the trends and challenges of interconnect design as the technology feature size rapidly decreases towards below 0.1 micron. Then, we present commonly used interconnect models and a set of interconnect design and optimization techniques for improving interconnect performance and reliability. Finally, we present comparisons of different optimization techniques in terms of their efficiency and optimization results, and show the impact of these optimization techniques on interconnect performance in each technology generation from the 0.35µm to 0.07µm projected in the National Technology Roadmap for Semiconductors.
Efficient ReducedOrder Modeling of FrequencyDependent Coupling Inductances associated with 3D Interconnect Structures
, 1994
"... Reducedorder modeling techniques are now commonly used to efficiently simulate circuits combined with interconnect, but generating reducedorder models from realistic 3D structures has received less attention. In this paper we describe a Krylovsubspace based method for deriving reducedorder mode ..."
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Cited by 64 (12 self)
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Reducedorder modeling techniques are now commonly used to efficiently simulate circuits combined with interconnect, but generating reducedorder models from realistic 3D structures has received less attention. In this paper we describe a Krylovsubspace based method for deriving reducedorder models directly from the 3D magnetoquasistatic analysis program FastHenry. This new approach is no more expensive than computing an impedance matrix at a single frequency.
Reducedorder modeling techniques based on Krylov subspaces and their use in circuit simulation
, 1998
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Determination of worstcase aggressor alignment for delay calculation
 In Proc. of the IEEE International Conference on ComputerAided Design (ICCAD
, 1998
"... Increases in delay due to coupling can have a dramatic impact on IC performance for deep submicron technologies. To achieve maximum performance there is a need for analyzing logic stages with large complex coupled interconnects. In timing analysis, the worstcase delay of gates along a critical path ..."
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Cited by 38 (0 self)
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Increases in delay due to coupling can have a dramatic impact on IC performance for deep submicron technologies. To achieve maximum performance there is a need for analyzing logic stages with large complex coupled interconnects. In timing analysis, the worstcase delay of gates along a critical path must include the effect of noise due to switching of nearby aggressor gates. In this paper, we propose a new waveform iteration strategy to compute the delay in the presence of coupling and to align aggressor inputs to determine the worstcase victim delay. We demonstrate the application of our methodology at both the transistorlevel and celllevel. In addition, we prove that the waveforms generated in our methodology converge under typical timing analysis conditions. 1.
Stable and efficient reduction of large, multiport RC networks by pole analysis via congruence transformations,” submitted to
 IEEE Trans. ComputerAided Design
"... Abstract — A novel technique is presented which employs Pole Analysis via Congruence Transformations (PACT) to reduce RC networks in a wellconditioned manner. Pole analysis is shown to be more efficient than Padé approximations when the number of network ports is large, and congruence transformati ..."
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Cited by 35 (0 self)
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Abstract — A novel technique is presented which employs Pole Analysis via Congruence Transformations (PACT) to reduce RC networks in a wellconditioned manner. Pole analysis is shown to be more efficient than Padé approximations when the number of network ports is large, and congruence transformations preserve the passivity (and thus absolute stability) of the networks. Networks are represented by admittance matrices throughout the analysis, and this representation simplifies interfacing the reduced networks with circuit simulators as well as facilitates realization of the reduced networks using RC elements. A prototype SPICEin, SPICEout, network reduction CAD tool called RCFIT is detailed, and examples are presented which demonstrate the accuracy and efficiency of the PACT algorithm. 1.
An Efficient Lyapunov EquationBased Approach for Generating ReducedOrder Models of Interconnect
, 1999
"... In this paper we present a new algorithm for computing reducedorder models of interconnect which utilizes the dominant controllable subspace of the system. The dominant controllable modes are computed via a new iterative Lyapunov equation solver, Vector ADI. This new algorithm is as inexpensive as ..."
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Cited by 25 (5 self)
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In this paper we present a new algorithm for computing reducedorder models of interconnect which utilizes the dominant controllable subspace of the system. The dominant controllable modes are computed via a new iterative Lyapunov equation solver, Vector ADI. This new algorithm is as inexpensive as Krylov subspacebased moment matching methods, and often produces a better approximation over a wide frequency range. A spiral inductor and a transmission line example show this new method can be much more accurate than moment matching via Arnoldi.
Model Reduction of Large Linear Systems via Low Rank System Gramians
, 2000
"... This dissertation concerns the model reduction of large, linear, timeinvariant systems. A new method called the Dominant Gramian Eigenspaces method, which utilizes low rank approximations to the exact system gramians, is proposed for such system. The Cholesky Factor ..."
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Cited by 23 (0 self)
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This dissertation concerns the model reduction of large, linear, timeinvariant systems. A new method called the Dominant Gramian Eigenspaces method, which utilizes low rank approximations to the exact system gramians, is proposed for such system. The Cholesky Factor
PRIMO: probability interpretation of moments for delay calculation
 Proc. of Design Automation Conference
, 1998
"... Moments of the impulse response are widely used for interconnect delay analysis, from the explicit Elmore delay (first moment of the impulse response) expression, to moment matching methods which create reduced order transimpedance and transfer function approximations. However, the Elmore delay is f ..."
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Cited by 21 (0 self)
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Moments of the impulse response are widely used for interconnect delay analysis, from the explicit Elmore delay (first moment of the impulse response) expression, to moment matching methods which create reduced order transimpedance and transfer function approximations. However, the Elmore delay is fast becoming ineffective for deep submicron technologies, and reduced order transfer function delays are impractical for use as earlyphase design metrics or as design optimization cost functions. This paper describes an approach for fitting moments of the impulse response to probability density functions so that delays can be estimated from probability tables. For RC trees it is demonstrated that the incomplete gamma function provides a provably stable approximation. The step response delay is obtained from a onedimensional table lookup. 1