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

By M. Rewienski, Jacob K. White. IEEE/ACM International Conference on Computer Aided Design. ICCAD 2001. IEEE/ACM Digest of Technical Papers (Cat. No.01CH37281), 2001

628 citations recorded by the source corpus.

Subfields: Electronic, Optical and Magnetic Materials, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/209ab880ad76faf3389b605c72138241dd24eb31

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Citations in the corpus

An efficient reduced‐order modeling approach for non‐linear parametrized partial differential equations (2008, neutral): “In particular, linearization methods [27, 28, 29] and polynomial approximation methods [30, 31] have been proposed to treat certain (weakly) nonlinear problems quite satisfactorily.”
Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective (2014, methodology): “In [112], three different methods of approximating f(V z(t)) are analyzed and compared in detail: a polynomial approximation [57, 77, 159], an approximation by a weighted sum of low degree polynomials or linear functions [165] and an approximation (estimation) by DEIM interpolation [56].”
Missing Point Estimation in Models Described by Proper Orthogonal Decomposition (2008, positive): “This approach has been successfully applied to nonlinear analogue circuits and micromachined devices [35], [36], and to a nonlinear CFD model of a supersonic diffuser [21].”
Constraint reduction procedures for reduced‐order subsurface flow models based on POD–TPWL (2015, methodology): “We note that [20] and [47] also used the spectral radius of an amplification matrix as a stability indicator for piecewise linear reduced-order ODE systems.”
EFFICIENT REDUCED-BASIS TREATMENT OF NONAFFINE AND NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS (2007, background): “A large number of model order reduction (MOR) techniques [2, 7, 8, 22, 27, 32, 36, 41] have been developed to treat nonlinear time-dependent problems.”
Nonlinear Model Reduction via Discrete Empirical Interpolation (2010, methodology): “The TPWL approach was successfully applied to several practical nonlinear systems, especially in the circuit simulations [35, 36, 37, 40, 8].”
Use of reduced-order models in well control optimization (2017, methodology): “One reduced-order modeling procedure, referred to as POD-based trajectory piecewise linearization or POD-TPWL (Rewienski and White 2003), entails the combined use of the POD representation with linearization around saved states.”
A projection method for model reduction of bilinear dynamical systems (2006, background): “It is an active research topic to extend these Krylov subspace based projection methods to large scale nonlinear systems [20,3,9,19].”
Reduced-Order Models for MEMS Applications (2005, methodology): “Rewieński and White [20, 21] extended the basis set used to generate [T ] by incorporating the Krylov basis sets and the vectors {xi } at each of the linearization states {xi } along the training trajectory.”
Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations (2007, background): “The Proper Orthogonal Decomposition (POD) or Karhunen-Loève (KL) [72, 80] approach to sampling [75, 77, 97, 142] is immensely popular in a variety of contexts — turbulent flows [85], fluid-structure interaction [46], non-linear structural mechanics [73], turbo-machinery flows [156] — most notably in”
A comparison of model reduction techniques from structural dynamics, numerical mathematics and systems and control (2013, methodology): “Also, reduction methods for nonlinear dynamical systems (see e.g. [54,61]) fall outside the scope of this paper.”
Interpolation among reduced‐order matrices to obtain parameterized models for design, optimization and probabilistic analysis (2009, methodology): “An alternative can be found in the trajectory piecewise-linear method of Rewienski and White [19], which was developed to create ROMs of nonlinear systems.”
Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations (2007, background): “RB-like “snapshot” ideas are also found in some of the many Reduced Order Model (ROM) approaches in the temporal domain [14,38,39,89,116, 130 ,145,155,156]: POD sampling procedures are often invoked, and more recently greedy sampling approaches have also been considered [21].”