Asymptotic-preserving schemes for multiscale physical problems
We present the asymptotic transitions from microscopic to macroscopic physics, their
computational challenges and the asymptotic-preserving (AP) strategies to compute …
computational challenges and the asymptotic-preserving (AP) strategies to compute …
Hypocoercivity based sensitivity analysis and spectral convergence of the stochastic Galerkin approximation to collisional kinetic equations with multiple scales and …
In this paper we provide a general framework to study a general class of linear and
nonlinear kinetic equations with random uncertainties from the initial data or collision …
nonlinear kinetic equations with random uncertainties from the initial data or collision …
Uncertainty quantification for kinetic equations
Kinetic equations contain uncertainties in their collision kernels or scattering coefficients,
initial or boundary data, forcing terms, geometry, etc. Quantifying the uncertainties in kinetic …
initial or boundary data, forcing terms, geometry, etc. Quantifying the uncertainties in kinetic …
Solving the linear transport equation by a deep neural network approach
Uniform spectral convergence of the stochastic Galerkin method for the linear semiconductor Boltzmann equation with random inputs and diffusive scalings
In this paper, we study the generalized polynomial chaos (gPC) based stochastic Galerkin
method for the linear semiconductor Boltzmann equation under diffusive scaling and with …
method for the linear semiconductor Boltzmann equation under diffusive scaling and with …
A stochastic asymptotic-preserving scheme for the bipolar semiconductor Boltzmann-Poisson system with random inputs and diffusive scalings
In this paper, we study the bipolar Boltzmann-Poisson model, both for the deterministic
system and the system with uncertainties, with asymptotic behavior leading to the drift …
system and the system with uncertainties, with asymptotic behavior leading to the drift …
On the multi-species Boltzmann equation with uncertainty and its stochastic Galerkin approximation
In this paper the nonlinear multi-species Boltzmann equation with random uncertainty
coming from the initial data and collision kernel is studied. Well-posedness and long-time …
coming from the initial data and collision kernel is studied. Well-posedness and long-time …
High Order IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings
In this paper, we consider the high order method for solving the linear transport equations
under diffusive scaling and with random inputs. To tackle the randomness in the problem …
under diffusive scaling and with random inputs. To tackle the randomness in the problem …