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Multi-scale control variate methods for uncertainty quantification in kinetic equations
12 references·7 citing·31 second hop
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References

  • 2010Spectral Methods for Uncertainty Quantification953 cited
  • 2008A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data942 cited
  • 2010Spectral methods for uncertainty quantification : with applications to computational fluid dynamics572 cited
  • 2008Uncertainty quantification for systems of conservation laws177 cited
  • 2012Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions113 cited
  • 2013Uncertainty Quantification in Computational Fluid Dynamics103 cited
  • 2015Polynomial Chaos Methods for Hyperbolic Partial Differential Equations81 cited
  • 2013Robust Uncertainty Propagation in Systems of Conservation Laws with the Entropy Closure Method66 cited
  • 2016Polynomial Chaos Methods for Hyperbolic Partial Differential Equations: Numerical Techniques for Fluid Dynamics Problems in the Presence of Uncertainties46 cited
  • 2017Uncertainty Quantification for Hyperbolic and Kinetic Equations45 cited
  • 2017Multi-fidelity stochastic collocation method for computation of statistical moments39 cited
  • 2017A Stochastic Galerkin Method for the Boltzmann Equation with Multi-Dimensional Random Inputs Using Sparse Wavelet Bases38 cited

Cited by

  • 2021An Introduction to Uncertainty Quantification for Kinetic Equations and Related Problems28 cited

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  • 2020Multiscale Variance Reduction Methods Based on Multiple Control Variates for Kinetic Equations with Uncertainties25 cited
  • 2021Data-driven low-fidelity models for multi-fidelity Monte Carlo sampling in plasma micro-turbulence analysis19 cited
  • 2021Uncertainty Quantification for the BGK Model of the Boltzmann Equation Using Multilevel Variance Reduced Monte Carlo Methods19 cited
  • 2022Bi-fidelity stochastic collocation methods for epidemic transport models with uncertainties14 cited
  • 2022A bi-fidelity stochastic collocation method for transport equations with diffusive scaling and multi-dimensional random inputs11 cited
  • 2022Mean-field control variate methods for kinetic equations with uncertainties and applications to socioeconomic sciences8 cited