Inf-Sup-Constant-Free State Error Estimator for Model Order Reduction of Parametric Systems in Electromagnetics

Chellappa, Sridhar; Feng, Lihong; Rubia, Valentín de la; Benner, Peter

doi:10.1109/tmtt.2023.3288642

Cited by 4 publications

(23 citation statements)

References 46 publications

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“…It is discussed in [30] and [35] that the error estimators in [43] are theoretically less accurate than the estimators proposed in [29,35]. The error estimators in [43] more easily underestimate the true error than the estimators in [29,35], which is also numerically demonstrated in [29,35]. Here we review the error estimators proposed in our recent work [29,30,35].…”

Section: Error Estimators For Linear Steady Systemsmentioning

confidence: 92%

“…Some error estimators [29,30,35,43] for linear steady systems were proposed in order to avoid estimating/computing the spectral norm ∥M (µ) −1 ∥ involved in the error bounds in Subsection 3.2. An approach based on randomized residuals is proposed in [43], where some randomized systems are defined to get error estimators for both the sate error and the output error.…”

Section: Error Estimators For Linear Steady Systemsmentioning

confidence: 99%

“…, K, where ρk (µ) := ∥r k (µ)∥/∥r k (µ)∥ and Φk (µ) = ∥e du ∥ + ∥V du xdu (µ)∥ with e du := A t (µ) −1 r du (µ). Here, xdu (µ) and r du (µ) are defined in (34) and (35), respectively.…”

Section: Multi-fidelity Error Estimationmentioning

confidence: 99%

“…In order to evaluate the state error estimator, we also need to construct V e . In [35], we have explained how to construct V e in detail. In particular, a different criterion is used for greedy construction of V e , i.e.…”

Section: Computational Aspectsmentioning

confidence: 99%

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A Posteriori Error Estimation for Model Order Reduction of Parametric Systems

Feng,

Chellappa,

Benner

2023

Preprint

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This survey discusses a posteriori error estimation for model order reduction of parametric systems, including linear and nonlinear, time-dependent and steady systems. We focus on introducing the error estimators we have proposed in the past few years and comparing them with the most related error estimators from the literature. For a clearer comparison, we have translated some existing error bounds proposed in function spaces into the n-dimensional complex coordinate space and provide the corresponding proofs. Some new insights into our proposed error estimators are explored. Moreover, we review our newly proposed error estimator for nonlinear time-evolution systems, which is applicable to reduced-order models solved by arbitrary time-integration solvers. Our recent work on multi-fidelity error estimation is also briefly discussed. Finally, we derive a new inf-sup-constant-free output error estimator for nonlinear time-evolution systems. Numerical results for two examples show the robustness of the new error estimator.

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Section: Error Estimators For Linear Steady Systemsmentioning

confidence: 92%

Section: Error Estimators For Linear Steady Systemsmentioning

confidence: 99%

Section: Multi-fidelity Error Estimationmentioning

confidence: 99%

Section: Computational Aspectsmentioning

confidence: 99%

See 2 more Smart Citations

A Posteriori Error Estimation for Model Order Reduction of Parametric Systems

Feng,

Chellappa,

Benner

2023

Preprint

Self Cite

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“…• Theorem 7. It quantifies the state error estimator proposed in [38] with computable upper and lower bounds. • "Inf-sup-constant-free error estimator for time-evolution systems" section.…”

Section: Introductionmentioning

confidence: 99%

A posteriori error estimation for model order reduction of parametric systems

Feng,

Chellappa,

Benner

2024

Adv. Model. and Simul. in Eng. Sci.

Self Cite

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This survey discusses a posteriori error estimation for model order reduction of parametric systems, including linear and nonlinear, time-dependent and steady systems. We focus on introducing the error estimators we have proposed in the past few years and comparing them with the most related error estimators from the literature. For a clearer comparison, we have translated some existing error bounds proposed in function spaces into the vector space $${\mathbb {C}}^n$$ C n and provide the corresponding proofs in $$\mathbb C^n$$ C n . Some new insights into our proposed error estimators are explored. Moreover, we review our newly proposed error estimator for nonlinear time-evolution systems, which is applicable to reduced-order models solved by arbitrary time-integration solvers. Our recent work on multi-fidelity error estimation is also briefly discussed. Finally, we derive a new inf-sup-constant-free output error estimator for nonlinear time-evolution systems. Numerical results for three examples show the robustness of the new error estimator.

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Improved a posteriori error bounds for reduced port-Hamiltonian systems

Rettberg,

Wittwar,

Buchfink

et al. 2024

Adv Comput Math

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Projection-based model order reduction of dynamical systems usually introduces an error between the high-fidelity model and its counterpart of lower dimension. This unknown error can be bounded by residual-based methods, which are typically known to be highly pessimistic in the sense of largely overestimating the true error. This work applies two improved error bounding techniques, namely (a) a hierarchical error bound and (b) an error bound based on an auxiliary linear problem, to the case of port-Hamiltonian systems. The approaches rely on a secondary approximation of (a) the dynamical system and (b) the error system. In this paper, these methods are adapted to port-Hamiltonian systems. The mathematical relationship between the two methods is discussed both theoretically and numerically. The effectiveness of the described methods is demonstrated using a challenging three-dimensional port-Hamiltonian model of a classical guitar with fluid–structure interaction.

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Inf-Sup-Constant-Free State Error Estimator for Model Order Reduction of Parametric Systems in Electromagnetics

Cited by 4 publications

References 46 publications

A Posteriori Error Estimation for Model Order Reduction of Parametric Systems

A Posteriori Error Estimation for Model Order Reduction of Parametric Systems

A posteriori error estimation for model order reduction of parametric systems

Improved a posteriori error bounds for reduced port-Hamiltonian systems

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