23 research outputs found
A combination between the reduced basis method and the ANOVA expansion: On the computation of sensitivity indices
No full textWe consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance of a three-step RB-ANOVA-RB method. This is a combination of the reduced basis (RB) method and the analysis of variations (ANOVA) expansion, aiming at compressing the parameter space without affecting the accuracy of the output. The idea of this method is to compute a first (coarse) RB approximation of the output of interest involving all the parameter components, but with a large tolerance on the a posteriori error estimate; then, we evaluate the ANOVA expansion of the output and freeze the least important parameter components; finally, considering a restricted model involving just the retained parameter components, we compute a second (fine) RB approximation with a smaller tolerance on the a posteriori error estimate. The fine RB approximation entails lower computational costs than the coarse one, because of the reduction of parameter dimensionality. Our result provides a criterion to avoid the computation of those terms in the ANOVA expansion that are related to the interaction between parameters in the bilinear form, thus making the RB-ANOVA-RB procedure computationally more feasible. © 2013 Académie des sciences
Certified Reduced Basis Method for Affinely Parametric Isogeometric Analysis NURBS Approximation
No full textIn this work we apply reduced basis methods for parametric PDEs to an isogeometric formulation based on NURBS. We propose an integrated and complete work pipeline from CAD to parametrization of domain geometry, then from full order to certified reduced basis solution. IsoGeometric Analysis (IGA), as well as reduced basis methods for parametric PDEs growing research themes in scientific computing and computational mechanics. Their combination enhances the solution of some class of problems, especially the ones characterized by parametrized geometries. This work shows that it is also possible for some class of problems to deal with affine geometrical parametrization combined with a NURBS IGA formulation. In this work we show a certification of accuracy and a complete integration between IGA formulation and parametric certified greedy RB formulation by introducing two numerical examples in heat transfer with different parametrization
Certified Reduced Basis Method for Parametrized Partial Differential Equations: a Combination with ANOVA Expansion
No full textIn many fields, the computation of an output depending on a field variable is of great interest. If the field variable depends on a high-dimensional parameter, the computational cost involved can be huge. Hence, it is necessary to find efficient and reliable methods to solve such a problem. In this report, we describe a method to solve in an efficient and reliable way elliptic coercive parametric partial differential equations which depend on high-dimensional parameters. The idea is to combine two methods already known, the Reduced Basis (RB) method and the ANOVA expansion. Since also the use of the Reduced Basis method for the approximation of high-dimensional parametric partial differential equations can be computationally expensive, it is important to find a method to approximate the solution in an efficient way. The method is divided in three steps, RB-ANOVA-RB. First, we use the Reduced Basis method with a big tolerance to have a coarse approximation of the output of interest. This allows us to use the ANOVA expansion in order to determine if there exists some less important parameters. If it is the case, we freeze them and then reapply the Reduced Basis method with a low tolerance to get a fine approximation of the output.CMCSSemester project, Mathematics project I
Reduced Basis Approximation for the Structural-Acoustic Design based on Energy Finite Element Analysis (RB-EFEA)
No full textIn many engineering applications, the investigation of the vibro-acoustic response of
structures is of great interest. Hence, great effort has been dedicated to improve methods
in this field in the last twenty years. Classical techniques have the main drawback that
they become unaffordable when high frequency impact waves are considered. In that sense,
the Energy Finite Element Analysis (EFEA) is a good alternative to those methods. Based on
an approximate model, EFEA gives time and locally space-averaged energy densities and has
been proven to yield accurate results.
However, when dealing with structural-acoustic design, it is necessary to obtain the
energy density varying a large number of parameters. It is computationally unaffordable
and too expensive to compute such solutions for each set of parameters. To prevent this
drawback, we introduce a reduced order model which allows to drastically decrease those
computational costs, while yielding a reliable and accurate approximation. In this paper,
we present an approximation of the EFEA solution considering the Reduced Basis (RB)
method. The RB method has already been applied successfully to many different problems. A
complete development of this procedure in the context of EFEA is introduced here.
Numerical tests and examples are provided for both geometrical and physical
parameters
Rejoinder on: Deville and Särndal’s calibration: revisiting a 25-year-old successful optimization problem
No full textSpace–time hp-approximation of parabolic equations
No full textISSN:1126-5434ISSN:0008-0624ISSN:0008-062
Transition Between Condensed Phases In Si And Ge
No full textABSTRACTThe thermodynamic interrelation between the amorphous semiconducting (a-sc), the diamond cubic (c-sc) and the liquid metal (lm) states of Ge and Si is reviewed with especial emphasis on the question of the thermodynamic uniqueness of the a-sc state following its structural relaxation. The experience on the occurrence of the direct lm→a-sc transition and its reverse is surveyed and interpreted. This experience, in conjunction with the lm undercooling studies of Devaud and the author, indicates that the formation, in the metastable regime, of a-sc from lm results from preferential growth rather than preferential nucleation.</jats:p
Comparative study of RANS-EDC, LES-CSE and LES-FGM simulations of Delft jet-in-hot-coflow (DJHC) natural gas flames
No full textWe report on a comparative study of model predictions of jet-in-hot-coflow flames. TheDelft Jet-in-Hot- Coflow (DJHC) burner was built to mimic the important characteristics of flameless combustion without the complications of a real furnace [1,2]. The DJHC burner has been used to create a turbulent diffusion flame of Dutch Natural Gas in a coflowing oxidizer stream of high temperature with low oxygen concentration. The experimental database contains the results of high speed chemiluminescence imaging, velocity statistics from LDA measurementsand temperature statistics from CARS measurements. In recent years several computational studies have been made using the DJHC burner as validation database [3-9]. It has been shown before that predictions are sensitive to the coflow radial profiles of temperature and oxygen concentration, to there presentation of effects of entrained air, and to turbulence-chemistry interaction and this is also the focus of the present study Fluid Mechanic
Author Correction: Acute thiamethoxam toxicity in honeybees is not enhanced by common fungicide and herbicide and lacks stress-induced changes in mRNA splicing (Scientific Reports, (2019), 9, 1, (19196), 10.1038/s41598-019-55534-8)
No full textThe original version of this Article contained an error in Figure 5A, where the gene structure was incorrectly labelled. The original Figure 5 and accompanying legend appear below. The original Article has been corrected.Universidade Estadual Paulista (UNESP) Instituto de Biociências Centro de Estudos de Insetos SociaisSchool of Biosciences College of Life and Environmental Sciences University of Birmingham, EdgbastonResearch Center On Animal Cognition Center for Integrative Biology Toulouse University CNRS UPSSchool of Biosciences University of NottinghamMRC Centre for Molecular Bacteriology and Infection and Department of Life Sciences Imperial College London, Ground Floor, Flowers Building, South Kensington CampusUniversidade Estadual Paulista (UNESP) Instituto de Biociências Centro de Estudos de Insetos Sociai
