Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems

By Zhong-Zhi Bai. 2002

678 citations recorded by the source corpus.

Subfields: Numerical Analysis, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/09fa412e207ec253d79bc56b13a48a195eadd003

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Citations in the corpus

Nonlinear Model Reduction via Discrete Empirical Interpolation (2010, methodology): “forms of polynomial nonlinearities followed by POD-Galerkin projection [14, 15, 31, 6, 16, 10].”
An adaptive-order rational Arnoldi method for model-order reductions of linear time-invariant systems (2006, background): “Recent works have proposed Krylov subspace projection methods to avoid such numerical difficulties [4–14].”
A comparison of model reduction techniques from structural dynamics, numerical mathematics and systems and control (2013, background): “However, these reviews mainly focus on methods from the individual fields, i.e. they focus on methods from structural dynamics [11,13], systems and control [29] or numerical mathematics [4,22] only.”
A projection method for model reduction of bilinear dynamical systems (2006, background): “Krylov subspace based projection methods have made remarkable progresses and successes for model reduction of very large linear systems over the past decade, see for example [5,8,16,6,1].”
Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective (2014, methodology): “For survey papers on model reduction based on Krylov subspaces see, e.g. [ 11,77,88,89].”
Closed-loop control of an open cavity flow using reduced-order models (2009, methodology): “It has thus been quickly realized that the application of approximate and iterative algorithms (as reviewed, for example, in Bai 2002 and Freund 2003), as well as the a priori reduction of the number of degrees of freedom (see e.g. Antoulas, Sorensen & Gugercin 2001), are crucial techniques when…”
A New Technique For Reduced-Order Modelling of Linear Time-Invariant System (2017, methodology): “Furthermore, plenty of time domain order-reduction methods are available in the literature such as proper orthogonal decomposition [16] and Krylov subspace techniques [17] proposed for reduced-order modelling of large-scale dynamical systems.”
Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, methodology): “There are also methods based on Krylov subspaces to generate a reduced basis [67, 75], including multivariate Pad\'e approximations and tangential interpolation for linear systems [13, 17, 74, 87].”
Simulation process of flexible multibody systems with non-modal model order reduction techniques (2011, neutral): “[22] or [23].”
Certified Real-Time Solution of Parametrized Partial Differential Equations (2005, neutral): “time-domain model reduction procedures [19, 25, 36].”
Balanced Truncation Model Reduction for Large-Scale Systems in Descriptor Form (2005, methodology): “There exist various model reduction approaches for standard state space systems such as balanced truncation [32, 47, 54, 64, 76, 77], moment matching approximation [ 6 , 27, 29, 30], singular perturbation approximation [52] and optimal Hankel norm approximation [32].”
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.”
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems (2015, neutral): “Surveys on this class of model reduction methods can be found in [22, 101]; see also [14, 15, 30, 44, 202].”
Mor4ansys: Generating compact models directly from ANSYS models (2004, methodology): “The main difference of our approach with those in Refs [ 10 ], [11] is that the damping matrix is not employed at all during the generation of a low-dimensional basis V ,t hat is, the latter is built as the orthogonolized Krylov subspace K K−1M, K−1b . Nevertheless, the reduced damping ma-”