A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices

Rewieński, Michał; White, Jacob K.

doi:10.1109/tcad.2002.806601

Cited by 487 publications

(338 citation statements)

References 16 publications

(2 reference statements)

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“…Once V r and W r are obtained using the H ε 2 -approach outlined in Algorithm 2, we use these subspaces to reduce the original nonlinear system as shown in (2.4). See [19,23] for other approaches that derive useful information from linearized systems in order to reduce nonlinear systems.…”

Section: H εmentioning

confidence: 99%

Structure-preserving model reduction for nonlinear port-Hamiltonian systems

Beattie

Gugercin

2011

IEEE Conference on Decision and Control and European Control Conference

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Abstract. This paper presents a structure-preserving model reduction approach applicable to large-scale, nonlinear port-Hamiltonian systems. Structure preservation in the reduction step ensures the retention of port-Hamiltonian structure which, in turn, assures the stability and passivity of the reduced model. Our analysis provides a priori error bounds for both state variables and outputs. Three techniques are considered for constructing bases needed for the reduction: one that utilizes proper orthogonal decompositions; one that utilizes H 2 /H∞-derived optimized bases; and one that is a mixture of the two. The complexity of evaluating the reduced nonlinear term is managed efficiently using a modification of the discrete empirical interpolation method (deim) that also preserves portHamiltonian structure. The efficiency and accuracy of this model reduction framework are illustrated with two examples: a nonlinear ladder network and a tethered Toda lattice.Key words. nonlinear model reduction, proper orthogonal decomposition, port-Hamiltonian, H 2 approximation, structure preservation AMS subject classifications. 37M05, 65P10, 93A151. Introduction and Background. The modeling of complex physical systems often involves systems of coupled partial differential equations, which upon spatial discretization, lead to dynamical models and systems of ordinary differential equations with very large state-space dimension. This motivates model reduction methods that produce low dimensional surrogate models capable of mimicking the input/output behavior of the original system model. Such reduced-order models could then be used as proxies, replacing the original system model in various computationally intensive contexts that are sensitive to system order, for example as a component in a larger simulation. Dynamical systems frequently have structural features that reflect underlying physics and conservation laws characteristic of the phenomena modeled. Reduced models that do not share such key structural features with the original system may produce response artifacts that are "unphysical" and as a result, such reduced models may be unsuitable for use as dependable surrogates for the original system, even if they otherwise yield high response fidelity. The key system feature that we wish to retain in our reduced models will be port-Hamiltonian structure. In a certain sense, this will be an expression of system passivity.

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Section: H εmentioning

confidence: 99%

Structure-preserving model reduction for nonlinear port-Hamiltonian systems

Beattie

Gugercin

2011

IEEE Conference on Decision and Control and European Control Conference

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“…In this paper we present the application of two most promising nonlinear reduction methods on an academic diode chain model. These are the trajectory piecewise linear approach (TPWL) [3] and the proper orthogonal decomposition (POD) [4] supported by missing point estimation (MPE) technique [5].…”

Section: Introductionmentioning

confidence: 99%

Model Order Reduction for Nonlinear Differential Algebraic Equations in Circuit Simulation

Voß¹,

Verhoeven

Bechtold³

et al. 2008

Progress in Industrial Mathematics at ECMI 2006

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“…Mathematical model order reduction (MOR) aims to replace (1) by a system of much smaller dimension, which can be solved by suitable DAE solvers within acceptable time. In [1], we have demonstrated the application of two most promising nonlinear reduction methods, the trajectory piecewise linear approach (TPWL) [2] and the proper orthogonal decomposition (POD) [3] on an academic diode chain model. In this paper we propose a different, in our opinion, more efficient approach, of combining the both methods.…”

Section: Introductionmentioning

confidence: 99%