Parametric Families of Reduced Finite Element Models. Theory and Applications

Balmès, Étienne

doi:10.1006/mssp.1996.0027

Cited by 125 publications

(100 citation statements)

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“…One solution successfully employed in aeroelasticity is the fictitious mass method [27], which has been used as a global basis for aeroelastic analyses with structural modifications in [28]. In this work, the basis + is built following a multi-model approach [29], where the baseline modes and the modes of the modified structure at a number of representative design points in the parameter space are retained. These additional design points are selected by perturbing independently each of the design parameter to their upper limit, with the others being kept constant at their nominal value.…”

Section: Generalized Coordinates For Aeroelastic Analysis With Structmentioning

confidence: 99%

“…the matrices can be explicitly expressed as I%J = + ∑ Ÿ 5 I%J Š w 5zU (29) so that the reduced matrices are quickly computed at each % ž and the construction and subsequent reduction through projection of a new FOM is avoided. The interpolation of the locally reduced transfer functions, and of the locally reduced state-space matrices, do not suffer from this limitation and thus are more convenient for a generic nonaffine parameter dependency, which is indeed the case of the aeroservoelastic system of Eq.…”

Section: Parametric Model Order Reductionmentioning

confidence: 99%

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Parametric reduced order model approach for rapid dynamic loads prediction

Castellani¹,

Lemmens

Cooper³

2016

Aerospace Science and Technology

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A parametric reduced order methodology for loads estimation is described that produces a fast and accurate prediction of gust and manoeuvre loads for different flight conditions and structural parameter variations. The approach enables efficient prediction of the peak loads whilst maintaining the correlated time histories for different loads. It is then possible to determine correlated loads plots with reduced computation without losing accuracy. The effectiveness of the methodology is demonstrated by considering loads arising from families of gusts and pitching manoeuvres acting upon a numerical transport aircraft aeroservoelastic model with varying flight conditions and structural properties.

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Section: Generalized Coordinates For Aeroelastic Analysis With Structmentioning

confidence: 99%

Section: Parametric Model Order Reductionmentioning

confidence: 99%

Parametric reduced order model approach for rapid dynamic loads prediction

Castellani¹,

Lemmens

Cooper³

2016

Aerospace Science and Technology

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“…These early methods were typically rather local and low-dimensional in parameter. In [3], Balmes first applied RB methods to general multi-parameter problems.…”

Section: Reduced Basis Backgroundmentioning

confidence: 99%

Reduced Basis Approximation and Error Bounds for Potential Flows in Parametrized Geometries

Rozza

2011

Commun. comput. phys.

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Abstract. In this paper we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for potential flows in affinely parametrized geometries. We review the essential ingredients: i) a Galerkin projection onto a lowdimensional space associated with a smooth "parametric manifold" in order to get a dimension reduction; ii) an efficient and effective greedy sampling method for identification of optimal and numerically stable approximations to have a rapid convergence; iii) an a posteriori error estimation procedure: rigorous and sharp bounds for the linearfunctional outputs of interest and over the potential solution or related quantities of interest like velocity and/or pressure; iv) an Offline-Online computational decomposition strategies to achieve a minimum marginal computational cost for high performance in the real-time and many-query (e.g., design and optimization) contexts. We present three illustrative results for inviscid potential flows in parametrized geometries representing a Venturi channel, a circular bend and an added mass problem.

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“…The affine representation (2) permits a "Construction-Evaluation" decomposition Balmes (1996); Machiels et al (2000); Prud'homme et al (2002) of computational effort that greatly reduces the marginal cost -relevant in the real-time and many-query contexts -of both the RB output evaluation, (7), and the associated error bound, (11). The expensive Construction stage, performed once, provides the foundation for the subsequent very inexpensive Evaluation stage, performed many times for each new desired µ ∈ D. We first consider the Construction-Evaluation decomposition for the output and then address the error bound.…”

Section: Construction-evaluation Decompositionmentioning

confidence: 99%

Reduced Basis Approximation and a Posteriori Error Estimation for Parametrized Parabolic PDEs: Application to Real‐Time Bayesian Parameter Estimation

Nguyen

Rozza

Huynh

et al. 2010

Large‐Scale Inverse Problems and Quantification of Uncertainty

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In this chapter we consider reduced basis approximation and a posteriori error estimation for linear functional outputs of affinely parametrized linear and non-linear parabolic partial differential equations. The essential ingredients are Galerkin projection onto a low-dimensional space associated with a smooth "parametric manifold" -dimension reduction; efficient and effective Greedy and POD-Greedy sampling methods for identification of optimal and numerically stable approximations -rapid convergence; rigorous and sharp a posteriori error bounds (and associated stability factors) for the linear-functional outputs of interest -certainty; and Offline-Online computational decomposition strategies -minimum marginal cost for high performance in the real-time/embedded (e.g., parameter estimation, control) and many-query (e.g., design optimization, uncertainty quantification Boyaval et al. (2008)

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Parametric Families of Reduced Finite Element Models. Theory and Applications

Cited by 125 publications

References 0 publications

Parametric reduced order model approach for rapid dynamic loads prediction

Parametric reduced order model approach for rapid dynamic loads prediction

Reduced Basis Approximation and Error Bounds for Potential Flows in Parametrized Geometries

Reduced Basis Approximation and a Posteriori Error Estimation for Parametrized Parabolic PDEs: Application to Real‐Time Bayesian Parameter Estimation

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