Model reduction methods based on Krylov subspaces

Freund, Robert M.

doi:10.1017/cbo9780511550157.004

Cited by 54 publications

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“…Note that, in (16), M , D, and K are N 0 × N 0 matrices and F is an N 0 × m matrix. Here, N 0 is the sum of the number of non-datum nodes in the circuit and the number of voltage sources, and m denotes the number of all voltage and current sources.…”

Section: Rcl Circuit Equationsmentioning

confidence: 99%

“…Here, N 0 is the sum of the number of non-datum nodes in the circuit and the number of voltage sources, and m denotes the number of all voltage and current sources. We remark that N 0 is the state-space dimension of the linear dynamical system (16), and m is the number of inputs (and outputs) of (16). In general, the matrix M is singular, and thus the first equation of (16) is a system of integro-differential-algebraic equations (integro-DAEs).…”

Section: Rcl Circuit Equationsmentioning

confidence: 99%

“…The general problem of order reduction of a given linear dynamical system (16) is to determine a reduced state-space dimension n 0 and data (19) such that the corresponding reduced-order model (18) is a sufficiently accurate approximation of (16). A practical way of assessing the accuracy of reduced-order models is based on the concept of Laplace-domain transfer functions of linear dynamical systems.…”

Section: Model Order Reductionmentioning

confidence: 99%

“…We remark that N is the sum of the state-space dimension N 0 of the equivalent system of integro-DAEs (16) and the number of inductors of the RCL circuit. Note that, in (22), the input vector u(t) and the output vector y(t) are the same as in (16), namely the vectors defined in (14). In particular, both systems (16) and (22) have m inputs and m outputs.…”

Section: First-order Formulationmentioning

confidence: 99%

“…The first such technique was asymptotic waveform evaluation (AWE) [31], which uses explicit moment matching. More recently, the attention has moved to reduced-order models generated by means of Krylovsubspace algorithms, which avoid the typical numerical instabilities of explicit moment matching; see, e.g., the survey papers [14,15,16].…”

Section: Introductionmentioning

confidence: 99%

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Structure-Preserving Model Order Reduction of RCL Circuit Equations

Freund

2008

Mathematics in Industry

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Summary. In recent years, order-reduction techniques based on Krylov subspaces have become the methods of choice for generating macromodels of large multi-port RLC circuits. Despite the success of these techniques and the extensive research efforts in this area, for general RCL circuits, the existing Krylov subspace-based reduction algorithms do not fully preserve all essential structures of the given large RCL circuit. In this paper, we describe the problem of structure-preserving model order reduction of general RCL circuits, and we discuss two state-of-the-art algorithms, PRIMA and SPRIM, for the solution of this problem. Numerical results are reported that illustrate the higher accuracy of SPRIM vs. PRIMA. We also mention some open problems.

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Section: Rcl Circuit Equationsmentioning

confidence: 99%

Section: Rcl Circuit Equationsmentioning

confidence: 99%

Section: Model Order Reductionmentioning

confidence: 99%

Section: First-order Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Structure-Preserving Model Order Reduction of RCL Circuit Equations

Freund

2008

Mathematics in Industry

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Model Reduction of Large Scale Descriptor Systems Using Time Limited Gramians

Haider

Ghafoor

Imran

et al. 2017

Asian Journal of Control

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A new technique for model order reduction of large scale continuous linear time invariant descriptor systems in limited time interval is proposed. The concept of time limited Gramians for descriptor systems is introduced for applications involving analysis, design or optimization in specific time interval. Balanced truncation based on magnitudes of Hankel singular values of the computed Gramians is performed to obtain the reduced order models in limited time interval. An approximate solution of time limited projected Lyapunov equations is developed and Cholesky factorisation of time limited Gramians is performed. Moreover, stability conditions for reduced order system are stated and two algorithms for stability preservation of reduced order models are presented. Results certify the successful application of the proposed techniques.

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Approximate Gauss–Newton methods for optimal state estimation using reduced‐order models

Lawless

Nichols

Boess

et al. 2007

Numerical Methods in Fluids

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SUMMARYThe Gauss-Newton (GN) method is a well-known iterative technique for solving nonlinear least-squares problems subject to dynamical system constraints. Such problems arise commonly in optimal state estimation where the systems may be stochastic. Variational data assimilation techniques for state estimation in weather, ocean and climate systems currently use approximate GN methods. The GN method solves a sequence of linear least-squares problems subject to linearized system constraints. For very large systems, low-resolution linear approximations to the model dynamics are used to improve the efficiency of the algorithm. We propose a new method for deriving low-order system approximations based on model reduction techniques from control theory. We show how this technique can be combined with the GN method to retain the response of the dynamical system more accurately and improve the performance of the approximate GN method.

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Model reduction methods based on Krylov subspaces

Cited by 54 publications

References 0 publications

Structure-Preserving Model Order Reduction of RCL Circuit Equations

Structure-Preserving Model Order Reduction of RCL Circuit Equations

Model Reduction of Large Scale Descriptor Systems Using Time Limited Gramians

Approximate Gauss–Newton methods for optimal state estimation using reduced‐order models

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