2019
DOI: 10.1016/j.cma.2018.10.047
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A non-intrusive B-splines Bézier elements-based method for uncertainty propagation

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Cited by 13 publications
(9 citation statements)
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“…In a real case scenario, we launch several hundred simulations by sampling the parameters, such as the inflow rate or Manning's number. The goal is to build a database and then perform statistical studies like those in Abdedou and Soulaimani (2018). This database can also be used to train machine learning algorithms, as in Jacquier et al (2021).…”
Section: Visualization Of the Flood Linesmentioning
confidence: 99%
“…In a real case scenario, we launch several hundred simulations by sampling the parameters, such as the inflow rate or Manning's number. The goal is to build a database and then perform statistical studies like those in Abdedou and Soulaimani (2018). This database can also be used to train machine learning algorithms, as in Jacquier et al (2021).…”
Section: Visualization Of the Flood Linesmentioning
confidence: 99%
“…This approach belongs to the multi-element techniques that use local piecewise bases expressed as a function of input random parameters. It is worth noting that the basic framework of the BSBEM in its full-order version has been presented in detail in [33,34]. Thus, only a summary description of its fundamental aspects is outlined in the following.…”
Section: Regression-based Non-intrusive B-splines Bézier Elements Met...mentioning
confidence: 99%
“…where e stands for the e th Bézier element I e and p i denotes the polynomial order of the univariate B-splines basis function ψ i (ξ i ). Details of the construction of the B-splines basis and their extraction from the local Bernstein's functions can be found in [33,34,36]. In each Bézier element, a set of n e s ≥ n b collocation points are selected ξ e(r) ∈ I e ; r = 1, .…”
Section: Let Us Considermentioning
confidence: 99%
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“…Finally, B-splines basis functions have also been used for uncertainty propagation to overcome the limitations of classical approaches in the presence of discontinuities (see e.g. [33,34]).…”
Section: Introductionmentioning
confidence: 99%