scholarly journals Stochastic reduced order computational model of structures having numerous local elastic modes in low frequency dynamics

2013 ◽  
Vol 332 (16) ◽  
pp. 3667-3680 ◽  
Author(s):  
A. Arnoux ◽  
A. Batou ◽  
C. Soize ◽  
L. Gagliardini
Keyword(s):  
Computational Model ◽  
Low Frequency ◽  
Reduced Order ◽  
Elastic Modes

scholarly journals Reduced-Order Computational Model for Low-Frequency Dynamics of Automobiles

2013 ◽  
Vol 5 ◽  
pp. 310362
Author(s):  
A. Arnoux ◽  
C. Soize ◽  
A. Batou ◽  
L. Gagliardini
Keyword(s):  
Computational Model ◽  
Low Frequency ◽  
Reduced Order

scholarly journals Stochastic Reduced-Order Model in Low-Frequency Dynamics in Presence of Numerous Local Elastic Modes

2011 ◽  
Vol 78 (6) ◽  
Author(s):  
C. Soize ◽  
A. Batou
Keyword(s):  
Structural Dynamics ◽  
Complex Structure ◽  
Probabilistic Approach ◽  
Low Frequency ◽  
Reduced Order Model ◽  
Frequency Range ◽  
Order Model ◽  
Reduced Order ◽  
Global Modes ◽  
Elastic Modes

This paper deals with the nonusual case in structural dynamics for which a complex structure exhibits both the usual global elastic modes and numerous local elastic modes in the low-frequency range. Despite the presence of these local elastic modes, we are interested in constructing a stochastic reduced-order model using only the global modes and in taking into account the local elastic modes with a probabilistic approach. In the first part, a formulation and an algorithm, which allow the “global elastic modes” and the “local elastic modes” to be calculated, are presented. The second part is devoted to the construction of the stochastic reduced-order model with the global elastic modes and in taking into account the uncertainties on the effects of the local elastic modes by the nonparametric probabilistic approach. Finally, an application, which validates the proposed theory is presented.

Modal Reduction of Mathematical Models of Biological Molecules

2005 ◽  
Author(s):  
Aiqin Li ◽  
Earl H. Dowell
Keyword(s):  
Low Frequency ◽  
Biological Molecules ◽  
Computational Time ◽  
Strong Nonlinearity ◽  
Reduced Order ◽  
Modal Reduction ◽  
Modal Synthesis ◽  
Frequency Excitation ◽  
A Chain ◽  
Proper Orthogonal

This paper reports a detailed study of modal reduction based on either linear normal mode(LNM) analysis or proper orthogonal decomposition(POD) for modeling a single α-D glucopyranose monomer as well as a chain of monomers. Also a modal reduction method combining POD and component modal synthesis(CMS) is developed. The accuracy and efficiency of these methods are reported. The focus of this study is to determine to what extent these methods can reduce the time and cost of molecular modeling and simultaneously provide the required accuracy. It has been demonstrated that a linear reduced order model(ROM) is valid for small amplitude excitation and low frequency excitation. It is found that a nonlinear ROM based on POD modes provides a good approximation even for large excitation while the nonlinear ROM using linear eigenmodes as the basis vectors is less effective for modeling molecules with a strong nonlinearity. The ROM based on CMS using POD modes for each component also gives a good approximation. With the reduction in the dimension of the system using these methods the computational time and cost can be reduced significantly.

A Minimal Order Model From Zero to High Frequencies for Finite-Element Based Analysis of General 3-D Electromagnetic Problems

2013 ◽  
Author(s):  
Feng Sheng ◽  
Dan Jiao
Keyword(s):  
Finite Element ◽  
Low Frequency ◽  
Electromagnetic Analysis ◽  
Reduced Order Models ◽  
Minimal Order ◽  
Order Model ◽  
Package Design ◽  
High Frequencies ◽  
Reduced Order ◽  
Right Hand

Modern integrated circuits (IC) and package design has scaled into the deep submicron regime and the nanometer regime. Fast and broadband frequency-domain electromagnetic analysis has become increasingly important. The large problem size encountered in the analysis of ICs and packages is a major challenge especially for a finite element method (FEM) based electromagnetic analysis. To reduce the computational cost for large-scale electromagnetic analysis, model order reduction (MOR) methods have been developed to preprocess the huge linear system into reduced order models. However, in order to meet the modeling and simulation challenges arising from the IC and package design, existing MOR methods still have to overcome the following shortcomings. First, many existing MOR methods lack a closed-form error bound. Given an accuracy requirement, the model generated from existing methods may not be compact enough. Second, most of the existing reduced order models depend on frequency and right hand side. They lose efficiency when analyzing frequency-dependent problems with a large number of right hand sides. Last but not least, many existing MOR methods suffer from low frequency breakdown problem. Additional models have to be built if low frequency solutions, including DC solution, are required. This paper proposes a minimal order model for any prescribed accuracy for the finite element based solution of general 3-D problems having arbitrary lossless/lossy structures and inhomogeneous materials. This model entails no theoretical approximations. It is frequency and right hand side independent, and hence can be employed for both fast frequency and right hand side sweep. Moreover, the model does not suffer from low-frequency breakdown and is accurate from zero to high frequencies. To facilitate the application of such a minimal order model, we have also developed an efficient algorithm to generate this model. Numerical experiments have demonstrated the accuracy and efficiency of the proposed method. In addition to frequency-domain analysis, the proposed model can also be used for fast time-domain analysis.

qgs: A flexible Python framework of reduced-order multiscale climate models

2021 ◽  
Author(s):  
Lesley De Cruz ◽  
Jonathan Demaeyer ◽  
Stéphane Vannitsem
Keyword(s):  
Open Source Software ◽  
Climate Models ◽  
Low Frequency ◽  
Atmospheric Dynamics ◽  
The Other ◽  
Research Use ◽  
Good Representation ◽  
Atmospheric Variability ◽  
Reduced Order ◽  
Low Frequency Variability

<p>In atmospheric and climate sciences, research and development is often first conducted with a simple idealized system like the Lorenz-<em>N</em> models (<em>N ∈</em> {63, 84, 96}) which are toy models of atmospheric variability. On the other hand, reduced-order spectral quasi-geostrophic models of the atmosphere with a sufficient number of modes offer a good representation of the dry atmospheric dynamics. They allow one to identify typical features of the atmospheric circulation, such as blocked and zonal circulation regimes, and low-frequency variability. However, these models are less often considered in literature, despite their demonstration of more realistic behavior.</p><p><strong>qgs</strong> (Demaeyer et al., 2020) aims to popularize these systems by providing a fast and easy-to-use Python framework for researchers and teachers to integrate this kind of model. The documentation makes it clear and efficient to handle the model, by explaining the equations and parameters and linking these to the code. </p><p>The choice to use Python was specifically made to facilitate its use in Jupyter Notebooks and with the multiple recent machine learning libraries that are available in this language.</p><p>In this talk, we will present the modeling capabilities of <strong>qgs</strong> and show its usage in a varieties of didactical and research use cases.</p><p><strong>Reference</strong></p><p>Demaeyer, J., De Cruz, L., & Vannitsem, S. (2020). qgs: A flexible Python framework of reduced-order multiscale climate models. Journal of Open Source Software, 5(56), 2597, https://doi.org/10.21105/joss.02597 .</p>

Reduced-Order Computational Model

2014 ◽  
pp. 54-66
Author(s):  
Roger Ohayon ◽  
Christian Soize
Keyword(s):  
Computational Model ◽  
Reduced Order
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