Arnoldy based passive model order reduction algorithm

Balk, Igor

doi:10.1109/epep.2000.895539

Cited by 6 publications

(5 citation statements)

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“…In order to prevent the situation when a reduced order model of a passive system exhibits nonphysical behavior (exhibits an instability, or generates energy), a number of approaches for extracting stable and passive reduced order models have been proposed, mostly in the context of linear circuits and interconnects [67], [77], [78], see also [7], [8], [19], [24], [28], [97], [98], [101], [119]. One of the most widely used ideas, exploited in algorithms such as PRIMA [77], [78] is that congruence transformations preserve definiteness of a matrix.…”

Section: Chapter 5 Stability and Passivity Preservation With Tpwl Modelsmentioning

confidence: 99%

“…Reduced order modeling has therefore been applied in a number of engineering disciplines. In electrical engineering MOR techniques were first developed for macromodeling lumped circuits and interconnects [7], [16], [17], [19], [28], [43], [44], [52], [64], [77], [78], [82]- [84], [86], [87], [97], [100], [101], [121]. Then, those techniques were extended and applied to distributed electronic systems, full-wave electromagnetic modeling of various structures (including e.g.…”

Section: Motivationmentioning

confidence: 99%

“…Owing to their robustness and low numerical cost, Krylov subspace algorithms proved very suitable for reduction of large-scale systems, and gained considerable popularity, especially in electrical engineering. A number of Krylov-based MOR algorithms have been developed, including techniques based on Lanczos method [11]- [13], [25], [26], [29], [30], [90], or Arnoldi algorithm [7], [8], [18] [28], [43], [44], [78], [88], [100], [101], [110], [113], [117]- [119]. The main drawbacks of those methods are, in general, lack of provable error bounds for the extracted reduced models, and no guarantees of preserving stability or passivity of the original system.…”

Section: Previous Work On Model Order Reductionmentioning

confidence: 99%

“…e.g. PRIMA algorithm [67], [77], [78], see also [7], [8], [19], [24], [28], [97], [98], [101], [119]. Also, some efforts have been been undertaken to develop error estimates for Krylov-based reduced models [5], [103].…”

Section: Previous Work On Model Order Reductionmentioning

confidence: 99%

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Nonlinear Dynamical Systems

Diks¹

1999

Nonlinear Time Series Analysis

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In this study we discuss the problem of Model Order Reduction (MOR) for a class of nonlinear dynamical systems. In particular, we consider reduction schemes based on projection of the original state-space to a lower-dimensional space e.g. by using Krylov methods. In the nonlinear case, however, applying a projection-based MOR scheme does not immediately yield computationally efficient macromodels. In order to overcome this fundamental problem, we propose to first approximate the original nonlinear system with a weighted combination of a small set of linearized models of this system, and then reduce each of the models with an appropriate projection method. The linearized models are generated about a state trajectory of the nonlinear system corresponding to a certain 'training' input.As demonstrated by results of numerical tests, the obtained trajectory quasi-piecewise-linear reduced order models are very cost-efficient, while providing superior accuracy as compared to existing MOR schemes, based on single-state Taylor's expansions. In this dissertation, the proposed MOR approach is tested for a number of examples of nonlinear dynamical systems, including micromachined devices, analog circuits (discrete transmission line models, operational amplifiers), and fluid flow problems. The tests validate the extracted models and indicate that the proposed approach can be effectively used to obtain system-level models for strongly nonlinear devices.This dissertation also shows an inexpensive method of generating trajectory piecewise-linear (TPWL) models based on constructing the reduced models 'on-the-fly', which accelerates simulation of the system response. Moreover, we propose a procedure for estimating simulation errors, which can be used to determine accuracy of the extracted trajectory piecewise-linear reduced order models. Finally, we present projection schemes which result in improved accuracy of the reduced order TPWL models, as well as discuss approaches leading to guaranteed stable and passive TPWL reduced-order models. AcknowledgmentsFirst, I would like to thank Professor Jacob White, my advisor for the last four years, for introducing me to the world of nonlinear simulation and modeling. Learning from him, especially learning how to ask the right questions, has proved an invaluable experience. His guidance and encouragement made this work possible.I am also very grateful to my thesis committee members, Professors Karen Willcox and Alexandre Megretski for the numerous, fruitful, and often very animated discussions on nonlinear dynamical systems and model order reduction, which substantially deepened my understanding of this problem and its challenges, and their important suggestions which contributed to improving and broadening this dissertation.I would like to thank Luca Daniel and Prof. John Wyatt for interesting discussions on passivity preservation for nonlinear reduced order models, as well as Prof. Jaime Peraire, Prof. Steven Senturia, and Dr. Joel Phillips from Cadence, for their valuable commen...

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Section: Chapter 5 Stability and Passivity Preservation With Tpwl Modelsmentioning

confidence: 99%

Section: Motivationmentioning

confidence: 99%

Section: Previous Work On Model Order Reductionmentioning

confidence: 99%

Section: Previous Work On Model Order Reductionmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear Dynamical Systems

Diks¹

1999

Nonlinear Time Series Analysis

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“…In this paper we will give a brief overview of Arnoldi-based passive algorithm for reduction of 'full-wave' electromagnetic models [2,3] and then introduce MPI-based parallelization strategy.…”

Section: Introductionmentioning

confidence: 99%