Nonlinear Model Order Reduction in Nanoelectronics: Combination of POD and TPWL

Bechtold, Tamara; Striebel, Michael; Mohaghegh, Kasra; Maten, ter Ejw Jan

doi:10.1002/pamm.200810057

Cited by 12 publications

(8 citation statements)

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“…These linearization points are selected using prior knowledge from a training trajectory (or its approximation) of the full-order nonlinear system [72]. The TPWL approach was successfully applied to several practical nonlinear systems, especially in circuit simulations [71,72,73,89,12].…”

Section: Techniques For Nonlinearitiesmentioning

confidence: 99%

Nonlinear Model Reduction via Discrete Empirical Interpolation

Chaturantabut¹,

Sorensen²

2010

SIAM J. Sci. Comput.

1,649

1,778

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Section: Techniques For Nonlinearitiesmentioning

confidence: 99%

Nonlinear Model Reduction via Discrete Empirical Interpolation

Chaturantabut¹,

Sorensen²

2010

SIAM J. Sci. Comput.

1,649

1,778

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“…Originally Rewieński [33] proposed the usage of Krylov-based 5 [29]. For comparison between TPWL and POD (see Section 5.1.3.2), see [7,42].…”

Section: Reducing the Systemmentioning

confidence: 99%

“…Their span actually forms a POD-subspace (see Section 5.1.3.2) that is collected on-the-fly within TPWL. The inclusion reduces the error of the solution of the reduced model [7]. The final reduced subspace is then spanned by the r dominating left singular vectors, subsumed in V ∈ R n×r .…”

Section: Reducing the Systemmentioning

confidence: 99%

Advanced Topics in Model Order Reduction

Harutyunyan¹,

Ionutiu²,

Maten³

et al. 2015

Mathematics in Industry

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This Chapter contains three advanced topics in model order reduction (MOR): nonlinear MOR, MOR for multi-terminals (or multi-ports) and finally an application in deriving a nonlinear macromodel covering phase shift when coupling oscillators. The Sections are offered in a prefered order for reading, but can be read independentlty. terminal (or multi-port) problem. A crucial outcome of the research is that one should detect "important" internal unknowns, which one should not eliminate in order to keep a sparse reduced model. Such circuits come from verification problems, in which lots of parasitic elements are added to the original design. Analysis of effects due to parasitics is of vital importance during the design of large-scale integrated circuits, since it gives insight into how circuit performance is affected by undesired parasitic effects. Due to the increasing amount of interconnect and metal layers, parasitic extraction and simulation may become very time consuming or even unfeasible. Developments are presented, for reducing systems describing R and RC netlists resulting from parasitic extraction. The methods exploit tools from graph theory to improve sparsity preservation especially for circuits with multi-terminals. Circuit synthesis is applied after model reduction, and the resulting reduced netlists are tested with industrial circuit simulators. With the novel RC reduction method SparseMA, experiments show reduction of 95% in the number of elements and 46x speed-up in simulation time. Section 5.3, written by Davit Harutyunyan, Joost Rommes, E. Jan W. ter Maten and Wil H.A. Schilders, addresses the determination of phase shift when perturbing or coupling oscillators. It appears that for each oscillator the phase shift can be approximated by solving an additional scalar ordinary differential equation coupled to the main system of equations. This introduces a nonlinear coupling effect to the phase shift. That just one scalar evolution equation can describe this is a great outcome of Model Order Reduction. The motivation behind this example is described as follows. Design of integrated RF circuits requires detailed insight in the behavior of the used components. Unintended coupling and perturbation effects need to be accounted for before production, but full simulation of these effects can be expensive or infeasible. In this Section we present a method to build nonlinear phase macromodels of voltage controlled oscillators. These models can be used to accurately predict the behavior of individual and mutually coupled oscillators under perturbation at a lower cost than full circuit simulations. The approach is illustrated by numerical experiments with realistic designs. Model Order Reduction of Nonlinear Network Problems1 The dynamics of an electrical circuit can in general be described by a nonlinear, first order, differential-algebraic equation (DAE) system of the form:q(x(t)) + j(x(t)) + Bu(t) = 0, (5.1a)completed with the output mapping 1 Section 5.1 has been written by Michael Striebel and E. ...

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“…In order to overcome this weak nonlinearity limitation, TPWL approach was first proposed in [187] and then extended in several ways (e.g.) [171,172,[188][189][190][191][192][193][194][195][196][197][198]. The central idea in all these approaches is to use a collection of expansions around states visited by a given training trajectory.…”

Section: Bilinearization Reduction Methodsmentioning

confidence: 99%

“…Man's TBR. Proper Orthogonal Decomposition (POD) was also used in [194] as linear MOR kernel. For comparison of different linear MOR strategies when applied to problems in circuit simulation [201][202][203][204] can be referred to.…”

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confidence: 99%

Advanced Model-Order Reduction Techniques for Large Scale Dynamical Systems

Nouri¹

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Model Order Reduction (MOR) has proven to be a powerful and necessary tool for various applications such as circuit simulation. In the context of MOR, there are some unaddressed issues that prevent its efficient application, such as "reduction of multiport networks" and "optimal order estimation" for both linear and nonlinear circuits. This thesis presents the solutions for these obstacles to ensure successful model reduction of large-scale linear and nonlinear systems.This thesis proposes a novel algorithm for creating efficient reduced-order macromodels from multiport linear systems (e.g. massively coupled interconnect structures). The new algorithm addresses the difficulties associated with the reduction of networks with large numbers of input/output terminals, that often result in large and dense reduced-order models. The application of the proposed reduction algorithm leads to reduced-order models that are sparse and block-diagonal in nature. It does not assume any correlation between the responses at ports; and thereby overcomes the accuracy degradation that is normally associated with the existing (Singular Value Decomposition based) terminal reduction techniques.Estimating an optimal order for the reduced linear models is of crucial importance to ensure accurate and efficient transient behavior. Order determination is known to be a challenging task and is often based on heuristics. Guided by geometrical considerations, a novel and efficient algorithm is presented to determine the minimum sufficient order that ensures the ii accuracy and efficiency of the reduced linear models.The optimum order estimation for nonlinear MOR is extremely important. This is mainly due to the fact that, the nonlinear functions in circuit equations should be computed in the original size within the iterations of the transient analysis. As a result, ensuring both accuracy and efficiency becomes a cumbersome task. In response to this reality, an efficient algorithm for nonlinear order determination is presented. This is achieved by adopting the geometrical approach to nonlinear systems, to ensure the accuracy and efficiency in transient analysis.Both linear and nonlinear optimal order estimation methods are not dependent on any specific order reduction algorithm and can work in conjunction with any intended reduced modeling technique.iii First and foremost, I would sincerely like to express my gratitude to my supervisor, Professor Michel Nakhla. Without his guidance, this thesis would have been impossible. I appreciate his insight into numerous aspects of numerical simulation and circuit theory, as well as his enthusiasm, wisdom, care and attention. I have learned from him many aspects of science and life. Working with him was truly an invaluable experience.

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Nonlinear Model Order Reduction in Nanoelectronics: Combination of POD and TPWL

Cited by 12 publications

References 4 publications

Nonlinear Model Reduction via Discrete Empirical Interpolation

Nonlinear Model Reduction via Discrete Empirical Interpolation

Advanced Topics in Model Order Reduction

Advanced Model-Order Reduction Techniques for Large Scale Dynamical Systems

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