Lundi 5 juin 2023

Organisme intervenant (ou équipe pour les séminaires internes)
CEA Nouvelle-Aquitaine
Nom intervenant
Gaël Poëtte
Building and solving efficient reduced models for the uncertain linear Boltz-
man equation: applications to neutronics (keff ) and photonics

Many physical applications rely on Monte-Carlo (MC) codes to solve partial differential equations. The MC resolution implies the sampling of the variables (x, t, v) (position, time, velocity). The simulations are costly but the MC resolution is competitive due to the high dimensional (3(x) + 3(v) + 1(t) = 7) problem. The number of articles NMC controls the accuracy which is O( 1/\sqrt{NMC}). Obviously, propagating uncertainties with respect to different parameters X ∈ Rd is of great interest. We then often face a 7 + d dimensional problem. Non-intrusive methods are usually applied (use of N runs of a black box code). When applying any non-intrusive method to propagate uncertainties through an MC code, the physical space (x, t, v) and the uncertain space (X) are both explored thanks to two different designs. The first one has NMC particles to explore the space (x, t, v), the second one has N runs for the uncertain one X. The two MC samplings are tensorised: N × NMC particles are processed for an overall error O( 1/\sqrt NMC). An uncertainty propagation study is consequently costly. But MC designs should allow avoiding the tensorisation of the NMC particles and N runs [3, 4, 1, 2, 5, 6]: the main idea of this work is to sample the whole space (x, t, v, X) with the same MC design. This implies sampling X within the code, hence the intrusiveness of the approach. The benefit of the approach will be presented on neutronic (kef f ) and photonic applications.

[1] Jose Antonio Carrillo and Mattia Zanella. Monte Carlo gPC methods for diffusive kinetic flocking models with uncertainties . 2019. preprint. 
[2] Lorenzo Pareschi and Mattia Zanella. Monte Carlo stochastic Galerkin methods for the Boltzmann equation with uncertainties: space-homogeneous case, 03 2020. 
[3] GaĂ«l PoĂ«tte. A gPC-intrusive Monte Carlo scheme for the resolution of the uncertain linear Boltzmann equation. Journal of Computational Physics, 385:135 – 162, 2019. 
[4] GaĂ«l PoĂ«tte. Spectral convergence of the generalized polynomial chaos reduced model obtained from the uncertain linear boltzmann equation. Mathematics and Computers in Simulation, 177:24–45, 2020. 
[5] Gaël Poëtte. Efficient uncertainty propagation for photonics: Combining implicit semi-analog monte carlo (ismc) and monte carlo generalised polynomial chaos (mc-gpc). Journal of Computational Physics, page 110807, 2021. 
[6] Gaël Poëtte and Emeric Brun. Efficient uncertain keff computations with the monte carlo resolution of generalised polynomial chaos based reduced models. Journal of Computational Physics, 456:111007, 2022. 

Salle de réunion 142, bùtiment 210
Date du jour