Numerical Analysis of the Monte-Carlo Noise for the Resolution of the Deterministic and Uncertain Linear Boltzmann Equation (Comparison of Non-Intrusive gPC and MC-gPC)

Monte Carlo-generalized Polynomial Chaos (MC-gPC) has already been thoroughly studied in the literature. MC-gPC both builds a gPC based reduced model of partial differential equation (PDE) interest and solves it with an intrusive MC scheme order to propagate uncertainties. This captures behavior solution set PDEs subject some uncertain parameters modeled by random variables. is method, needs modifications code be applied. may considered drawback. But, on another hand, important computational gains obtained have observed many applications. The resolution Boltzmann investigated different ways: wellposedness proved, convergence respect truncation P theoretically numerically coupling nonlinear physics performed. But study noise remains, our knowledge, done. purpose this paper. We are interested understanding what can expected terms error estimations NMC, number particles. For this, we estimate variances non-intrusive MC-gPC, numerically, compare them several configurations for schemes (the semi-analog non-analog ones). results show that literature used solve present excess variance strategies comparable particle numbers NMC (even if remains acceptable competitive situations).