A bi-fidelity method for the multiscale Boltzmann equation with random parameters
From MaRDI portal
Publication:2222790
DOI10.1016/j.jcp.2019.108914zbMath1453.65360arXiv1905.09023OpenAlexW2945522450WikidataQ127018315 ScholiaQ127018315MaRDI QIDQ2222790
Publication date: 27 January 2021
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1905.09023
Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Gas dynamics (general theory) (76N15) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) PDEs with randomness, stochastic partial differential equations (35R60) Numerical solutions to stochastic differential and integral equations (65C30) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75)
Related Items (6)
Monte Carlo stochastic Galerkin methods for the Boltzmann equation with uncertainties: space-homogeneous case ⋮ A bi-fidelity stochastic collocation method for transport equations with diffusive scaling and multi-dimensional random inputs ⋮ Learning nonlocal constitutive models with neural networks ⋮ Bifidelity data-assisted neural networks in nonintrusive reduced-order modeling ⋮ Uncertainty Quantification for the BGK Model of the Boltzmann Equation Using Multilevel Variance Reduced Monte Carlo Methods ⋮ Bi-fidelity stochastic collocation methods for epidemic transport models with uncertainties
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients
- From the Boltzmann equation to the incompressible Navier-Stokes equations on the torus: a quantitative error estimate
- Practical error bounds for a non-intrusive bi-fidelity approach to parametric/stochastic model reduction
- Asymptotic-preserving methods for hyperbolic and transport equations with random inputs and diffusive scalings
- On the Cauchy problem for Boltzmann equations: Global existence and weak stability
- Sparse high order FEM for elliptic sPDEs
- Spectral-Lagrangian methods for collisional models of non-equilibrium statistical states
- Local Hilbert expansion for the Boltzmann equation
- The Boltzmann equation and its applications
- Uncertainty quantification for kinetic models in socio-economic and life sciences
- Uncertainty quantification for kinetic equations
- Uniform spectral convergence of the stochastic Galerkin method for the linear semiconductor Boltzmann equation with random inputs and diffusive scaling
- Adaptive multi-fidelity polynomial chaos approach to Bayesian inference in inverse problems
- Micro-macro decomposition based asymptotic-preserving numerical schemes and numerical moments conservation for collisional nonlinear kinetic equations
- Multi-scale control variate methods for uncertainty quantification in kinetic equations
- On stochastic Galerkin approximation of the nonlinear Boltzmann equation with uncertainty in the fluid regime
- Corrigendum to: ``Multi-fidelity non-intrusive polynomial chaos based on regression
- A stochastic asymptotic-preserving scheme for the bipolar semiconductor Boltzmann-Poisson system with random inputs and diffusive scalings
- Spectral convergence of the stochastic Galerkin approximation to the Boltzmann equation with multiple scales and large random perturbation in the collision kernel
- Greedy algorithms for reduced bases in Banach spaces
- Multifidelity importance sampling
- Uniformly stable numerical schemes for the Boltzmann equation preserving the compressible Navier-Stokes asymptotics
- A smooth transition model between kinetic and hydrodynamic equations
- A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources
- Optimal Model Management for Multifidelity Monte Carlo Estimation
- A Stochastic Collocation Algorithm with Multifidelity Models
- Stochastic Collocation Methods on Unstructured Grids in High Dimensions via Interpolation
- Computational Aspects of Stochastic Collocation with Multifidelity Models
- Stochastic galerkin and collocation methods for quantifying uncertainty in differential equations: a review
- Exponential Runge–Kutta Methods for Stiff Kinetic Equations
- A Stochastic Galerkin Method for the Boltzmann Equation with Multi-Dimensional Random Inputs Using Sparse Wavelet Bases
- Multilevel Monte Carlo Path Simulation
- Fast algorithms for computing the Boltzmann collision operator
- A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
- The fluid dynamic limit of the nonlinear boltzmann equation
- An Asymptotic Preserving Numerical Scheme for Kinetic Equations in the Low Mach Number Limit
- Fluid dynamic limits of kinetic equations II convergence proofs for the boltzmann equation
- Numerical Solution of the Boltzmann Equation I: Spectrally Accurate Approximation of the Collision Operator
- Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations
- Uniform regularity in the random space and spectral accuracy of the stochastic Galerkin method for a kinetic-fluid two-phase flow model with random initial inputs in the light particle regime
- Uniform Regularity for Linear Kinetic Equations with Random Input Based on Hypocoercivity
- Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling
- Numerical methods for kinetic equations
- Stochastic finite element methods for partial differential equations with random input data
- Hypocoercivity Based Sensitivity Analysis and Spectral Convergence of the Stochastic Galerkin Approximation to Collisional Kinetic Equations with Multiple Scales and Random Inputs
- Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations
- Remarks on the Acoustic Limit for the Boltzmann Equation
- Predicting the output from a complex computer code when fast approximations are available
- AN ADAPTIVE MULTIFIDELITY PC-BASED ENSEMBLE KALMAN INVERSION FOR INVERSE PROBLEMS
- A New Asymptotic Preserving Scheme Based on Micro-Macro Formulation for Linear Kinetic Equations in the Diffusion Limit
- Approximation of high-dimensional parametric PDEs
- A Fast Spectral Method for the Boltzmann Collision Operator with General Collision Kernels
- Numerical Passage from Kinetic to Fluid Equations
- A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
This page was built for publication: A bi-fidelity method for the multiscale Boltzmann equation with random parameters
