A gPC-intrusive Monte-Carlo scheme for the resolution of the uncertain linear Boltzmann equation
From MaRDI portal
Publication:2214670
DOI10.1016/j.jcp.2019.01.052zbMath1451.65006OpenAlexW2916752512MaRDI QIDQ2214670
Publication date: 10 December 2020
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jcp.2019.01.052
transportsensitivity analysisMonte Carlo methoduncertainty quantificationgeneralized polynomial chaosintrusive
Monte Carlo methods (65C05) Stochastic analysis applied to problems in fluid mechanics (76M35) PDEs with randomness, stochastic partial differential equations (35R60) Boltzmann equations (35Q20)
Related Items
On derivation and verification of a kinetic model for quantum vibrational energy of polyatomic gases in the gas-kinetic unified algorithm ⋮ Monte Carlo stochastic Galerkin methods for the Boltzmann equation with uncertainties: space-homogeneous case ⋮ Intrusive acceleration strategies for uncertainty quantification for hyperbolic systems of conservation laws ⋮ Efficient uncertain \(k_{\mathrm{eff}}\) computations with the Monte Carlo resolution of generalised polynomial chaos based reduced models ⋮ Efficient uncertainty propagation for photonics: combining implicit semi-analog Monte Carlo (ISMC) and Monte Carlo generalised polynomial chaos (MC-gPC) ⋮ 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) ⋮ Asymptotic-preserving neural networks for multiscale time-dependent linear transport equations ⋮ Stochastic Galerkin particle methods for kinetic equations of plasmas with uncertainties ⋮ Spectral convergence of the generalized polynomial chaos reduced model obtained from the uncertain linear Boltzmann equation ⋮ Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Shallow Water Equations ⋮ Multivariate error modeling and uncertainty quantification using importance (re-)weighting for Monte Carlo simulations in particle transport ⋮ Multigroup-like MC resolution of generalised polynomial chaos reduced models of the uncertain linear Boltzmann equation (+discussion on hybrid intrusive/non-intrusive uncertainty propagation)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A stochastic surrogate model approach applied to calibration of unstable fluid flow experiments
- High-order accurate Lagrange-remap hydrodynamic schemes on staggered Cartesian grids
- Uncertainty propagation using Wiener-Haar expansions
- Multi-resolution analysis of Wiener-type uncertainty propagation schemes
- Time-dependent generalized polynomial chaos
- Treatment of uncertain material interfaces in compressible flows
- Arbitrary high-order schemes for the linear advection and wave equations: application to hydrodynamics and aeroacoustics
- Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach
- Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach
- Life-time reliability based assessment of structures submitted to thermal fatigue
- Long-term behavior of polynomial chaos in stochastic flow simulations
- Uncertainty quantification for systems of conservation laws
- An efficient, robust, domain-decomposition algorithm for particle Monte Carlo
- Stochastic design optimization: application to reacting flows
- Multigroup particle transport in a moving material
- Stochastic finite element modelling in linear transient heat transfer
- Monte-Carlo methods for the transport and diffusion equations
- Efficient model reduction in nonlinear dynamics using the Karhunen-Loève expansion and dual-weighted-residual methods
- A new stochastic approach to transient heat conduction modeling with uncertainty.
- Variance reduction method for particle transport equation in spherical geometry
- An unsplit Monte-Carlo solver for the resolution of the linear Boltzmann equation coupled to (stiff) Bateman equations
- Ingredients for a general purpose stochastic finite elements implementation
- A discretization of the multigroup \(P_N\) radiative transfer equation on general meshes
- Uncertainty propagation in finite deformations--A spectral stochastic Lagrangian approach
- A stochastic particle-mesh scheme for uncertainty propagation in vortical flows
- Beyond Wiener-Askey expansions: handling arbitrary PDFs
- Karhunen-Loève approximation of random fields by generalized fast multipole methods
- The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals
- Robust Uncertainty Propagation in Systems of Conservation Laws with the Entropy Closure Method
- Uncertainty Propagation for Systems of Conservation Laws, High Order Stochastic Spectral Methods
- Solution of the Nonlinear Radiative Transfer Equations by a Fully Implicit Matrix Monte Carlo Method Coupled with the Rosseland Diffusion Equation via Domain Decomposition
- Stochastic heat transfer enhancement in a grooved channel
- Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
- Asymptotic analysis of transport processes
- Uniformly distributed sequences with an additional uniform property
- Inverse Problem Theory and Methods for Model Parameter Estimation
- Adaptive Anisotropic Spectral Stochastic Methods for Uncertain Scalar Conservation Laws
- Iterative Polynomial Approximation Adapting to Arbitrary Probability Distribution
- Adaptive Bayesian Inference for Discontinuous Inverse Problems, Application to Hyperbolic Conservation Laws
- Is Gauss Quadrature Better than Clenshaw–Curtis?
- A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems
- Solution of stochastic partial differential equations using Galerkin finite element techniques
- A stochastic projection method for fluid flow. I: Basic formulation
