scholarly journals A Least-Squares Finite Element Reduced Basis Method

2021 ◽  
Vol 43 (2) ◽  
pp. A1081-A1107
Author(s):  
Jehanzeb H. Chaudhry ◽  
Luke N. Olson ◽  
Peter Sentz
Keyword(s):  
Finite Element ◽  
Least Squares ◽  
Reduced Basis Method ◽  
Reduced Basis ◽  
Basis Method

How well do we know our models?

2020 ◽  
Author(s):  
Denise Degen ◽  
Karen Veroy ◽  
Mauro Cacace ◽  
Magdalena Scheck-Wenderoth ◽  
Florian Wellmann
Keyword(s):  
Finite Element ◽  
Surrogate Model ◽  
Sensitivity Study ◽  
Reduced Basis Method ◽  
Sensitivity Analyses ◽  
Model Parameters ◽  
Reduced Basis ◽  
Global Sensitivity ◽  
Sensitivity Studies ◽  
Basis Method

<p>In Geosciences, we face the challenge of characterizing uncertainties to provide reliable predictions of the earth surface to allow, for instance, a sustainable and renewable energy management. In order, to address the uncertainties we need a good understanding of our geological models and their associated subsurface processes.</p><p>Therefore, the essential pre-step for uncertainty analyses are sensitivity studies. Sensitivity studies aim at determining the most influencing model parameters. Hence, we require them to significantly reduce the parameter space to avoid unfeasibly large compute times.</p><p>We distinguish two types of sensitivity analyses: local and global studies. In contrast, to the local sensitivity study, the global one accounts for parameter correlations. That is the reason, why we employ in this work a global sensitivity study. Unfortunately, global sensitivity studies have the disadvantage that they are computationally extremely demanding. Hence, they are prohibitive even for state-of-the-art finite element simulations.</p><p>For this reason, we construct a surrogate model by employing the reduced basis method. The reduced basis method is a model order reduction technique that aims at significantly reducing the spatial and temporal degrees of freedom of, for instance, finite element solves. In contrast to other surrogate models, we obtain a surrogate model that preserves the physics and is not restricted to the observation space. As we will show, the reduced basis method leads to a speed-up of five to six orders of magnitude with respect to our original problem while retaining an accuracy higher than the measurement accuracy.</p><p>In this work, we elaborate on the advantages of global sensitivity studies in comparison to local ones. We use several case studies, from large-scale European sedimentary basins to demonstrate how the global sensitivity studies are used to learn about the influence of transient, such as paleoclimate effects, and stationary effects. We also demonstrate how the results can be used in further analyses, such as deterministic and stochastic model calibrations. Furthermore, we show how we can use the analyses to learn about the subsurface processes and to identify model short comes.</p>

scholarly journals An Improved Discrete Least-Squares/Reduced-Basis Method for Parameterized Elliptic PDEs

2018 ◽  
Vol 81 (1) ◽  
pp. 76-91
Author(s):  
Max Gunzburger ◽  
Michael Schneier ◽  
Clayton Webster ◽  
Guannan Zhang
Keyword(s):  
Least Squares ◽  
Reduced Basis Method ◽  
Elliptic Pdes ◽  
Reduced Basis ◽  
Basis Method

Structural Analysis Based on Coefficient Reduced-Basis Method

2014 ◽  
Vol 543-547 ◽  
pp. 46-49
Author(s):  
Yong Hong Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Analysis ◽  
Static Problem ◽  
Time Algorithm ◽  
Reduced Basis Method ◽  
Design Parameters ◽  
Reduced Basis ◽  
Linear Elastic ◽  
Basis Method

Efficiency and accuracy of forward problem are important in structural analysis. A real-time algorithm, called coefficient reduced-basis method, is applied to analyze a static problem. A truck frame is taken as an example. Results computed from finite element method, reduced-basis method and coefficient reduced-basis method are obtained. Comparing results from the three methods, coefficient reduced-basis method can get high-precision results quickly, which not separate the design parameters from the linear elastic operators.

Structural Dynamic Analysis Based on Inversion Reduced-Basis Method

2011 ◽  
Vol 94-96 ◽  
pp. 2039-2042
Author(s):  
Yong Hong Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Analysis ◽  
Dynamic Problem ◽  
Time Algorithm ◽  
Reduced Basis Method ◽  
Reduced Basis ◽  
Mass System ◽  
Structural Dynamic ◽  
Basis Method

Efficiency and accuracy of forward problem are important in structural analysis. A real-time algorithm, called inversion reduced-basis method (IRBM), is applied to analyze a dynamic problem. A spring-mass system is taken as an example, results computed from finite element method and IRBM are obtained. Comparing results from the two methods, IRBM can get high-precision results quickly.

EVALUATION OF FLUX INTEGRAL OUTPUTS FOR THE REDUCED BASIS METHOD

2010 ◽  
Vol 20 (03) ◽  
pp. 351-374 ◽  
Author(s):  
JENS L. EFTANG ◽  
EINAR M. RØNQUIST
Keyword(s):  
Finite Element ◽  
Second Order ◽  
Reduced Basis Method ◽  
Reduced Basis ◽  
Numerical Example ◽  
Output Error ◽  
Primal Dual ◽  
Basis Method

In this paper, we consider the evaluation of flux integral outputs from reduced basis solutions to second-order PDEs. In order to evaluate such outputs, a lifting function v⋆ must be chosen. In the standard finite element context, this choice is not relevant, whereas in the reduced basis context, as we show, it greatly affects the output error. We propose two "good" choices for v⋆ and illustrate their effect on the output error by examining a numerical example. We also make clear the role of v⋆ in a more general primal-dual reduced basis approximation framework.

scholarly journals An Enhanced Reduced Basis Method for Wideband Finite Element Method Simulations

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 60877-60884 ◽  
Author(s):  
Damian Szypulski ◽  
Grzegorz Fotyga ◽  
Michal Mrozowski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Reduced Basis Method ◽  
Reduced Basis ◽  
Basis Method ◽  
Element Method
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