175 citations · 346 across the 31 of their papers we have counts for
25 papers · 1 filter
Structure-preserving neural networks for the regularized entropy-based closure of the Boltzmann moment system
Steffen Schotthöfer, M. Paul Laiu, Martin Frank +1
The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations.…
A semi-implicit dynamical low-rank discontinuous Galerkin method for space homogeneous kinetic equations. Part I: emission and absorption
Peimeng Yin, Eirik Endeve, Cory D. Hauck +1
Dynamical low-rank approximation (DLRA) is an emerging tool for reducing computational costs and provides memory savings when solving high-dimensional problems. In this work, we pr…
A Collision-Based Hybrid Method for the BGK Equation
Minwoo Shin, Cory D. Hauck, Ryan G. McClarren
We apply the collision-based hybrid introduced in \cite{hauck} to the Boltzmann equation with the BGK operator and a hyperbolic scaling. An implicit treatment of the source term is…
Numerical analysis of a hybrid method for radiation transport
Andrés Galindo-Olarte, Victor P. DeCaria, Cory D. Hauck
In this work, we prove rigorous error estimates for a hybrid method introduced in [15] for solving the time-dependent radiation transport equation (RTE). The method relies on a spl…
A Predictor-Corrector Strategy for Adaptivity in Dynamical Low-Rank Approximations
Cory Hauck, Stefan Schnake
In this paper, we present a predictor-corrector strategy for constructing rank-adaptive dynamical low-rank approximations (DLRAs) of matrix-valued ODE systems. The strategy is a co…
Asymptotic Preserving Discontinuous Galerkin Methods for a Linear Boltzmann Semiconductor Model
Victor DeCaria, Cory Hauck, Stefan Schnake
A key property of the linear Boltzmann semiconductor model is that as the collision frequency tends to infinity, the phase space density converges to an isotropic fu…
Numerical schemes for a multi-species BGK model with velocity-dependent collision frequency
Jeffrey Haack, Cory Hauck, Christian Klingenberg +2
We consider a kinetic description of a multi-species gas mixture modeled with Bhatnagar-Gross-Krook (BGK) collision operators, in which the collision frequency varies not only in t…
Neural network-based, structure-preserving entropy closures for the Boltzmann moment system
Steffen Schotthöfer, Tianbai Xiao, Martin Frank +1
This work presents neural network based minimal entropy closures for the moment system of the Boltzmann equation, that preserve the inherent structure of the system of partial diff…
Conservative DG Method for the Micro-Macro Decomposition of the Vlasov-Poisson-Lenard-Bernstein Model
Eirik Endeve, Cory D. Hauck
The micro-macro (mM) decomposition approach is considered for the numerical solution of the Vlasov--Poisson--Lenard--Bernstein (VPLB) system, which is relevant for plasma physics a…
A structure-preserving surrogate model for the closure of the moment system of the Boltzmann equation using convex deep neural networks
Steffen Schotthöfer, Tianbai Xiao, Martin Frank +1
Direct simulation of physical processes on a kinetic level is prohibitively expensive in aerospace applications due to the extremely high dimension of the solution spaces. In this…
Data-driven, structure-preserving approximations to entropy-based moment closures for kinetic equations
William A. Porteous, M. Paul Laiu, Cory D. Hauck
We present a data-driven approach to construct entropy-based closures for the moment system from kinetic equations. The proposed closure learns the entropy function by fitting the…
Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering kernel
Qiwei Sheng, Cory D. Hauck
We present an error analysis for the discontinuous Galerkin method applied to the discrete-ordinate discretization of the steady-state radiative transfer equation. Under some mild…
Analysis of a new implicit solver for a semiconductor model
Victor P. DeCaria, Cory D. Hauck, M. Paul Laiu
We present and analyze a new iterative solver for implicit discretizations of a simplified Boltzmann-Poisson system. The algorithm builds on recent work that incorporated a sweepin…
Hybrid Solver for the Radiative Transport Equation Using Finite Volume and Discontinuous Galerkin
Vincent Heningburg, Cory D. Hauck
We propose a hybrid spatial discretization for the radiative transport equation that combines a second-order discontinuous Galerkin (DG) method and a second-order finite volume (FV…
Ray Effect Mitigation for the Discrete Ordinates Method Using Artificial Scattering
Martin Frank, Jonas Kusch, Thomas Camminady +1
Solving the radiative transfer equation with the discrete ordinates (S) method leads to a non-physical imprint of the chosen quadrature set on the solution. To mitigate these s…
Low-memory, discrete ordinates, discontinuous Galerkin methods for radiative transport
Zheng Sun, Cory D. Hauck
The discrete ordinates discontinuous Galerkin (-DG) method is a well-established and practical approach for solving the radiative transport equation. In this paper, we study a…
Diagnosing Forward Operator Error Using Optimal Transport
Michael A. Puthawala, Cory D. Hauck, Stanley J. Osher
We investigate overdetermined linear inverse problems for which the forward operator may not be given accurately. We introduce a new tool called the structure, based on the Wassers…
A Positive Asymptotic Preserving Scheme for Linear Kinetic Transport Equations
M. Paul Laiu, Martin Frank, Cory D. Hauck
We present a positive and asymptotic preserving numerical scheme for solving linear kinetic, transport equations that relax to a diffusive equation in the limit of infinite scatter…
A regularized entropy-based moment method for kinetic equations
Graham W. Alldredge, Martin Frank, Cory D. Hauck
We present a new entropy-based moment method for the velocity discretization of kinetic equations. This method is based on a regularization of the optimization problem defining the…
Positivity preserving DG schemes for a Boltzmann - Poisson model of electrons in semiconductors in curvilinear momentum coordinates
José A. Morales Escalante, Irene M. Gamba, Eirik Endeve +1
The work presented in this paper is related to the development of positivity preserving Discontinuous Galerkin (DG) methods for Boltzmann - Poisson (BP) computational models of ele…
Multiscale convergence properties for spectral approximations of a model kinetic equation
Zheng Chen, Cory D. Hauck
In this work, we prove rigorous convergence properties for a semi-discrete, moment-based approximation of a model kinetic equation in one dimension. This approximation is equivalen…
Scientific Data Interpolation with Low Dimensional Manifold Model
Wei Zhu, Bao Wang, Richard Barnard +3
We propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low…
A fast spectral method for the Boltzmann collision operator with general collision kernels
Irene M. Gamba, Jeffrey R. Haack, Cory D. Hauck +1
We propose a simple fast spectral method for the Boltzmann collision operator with general collision kernels. In contrast to the direct spectral method \cite{PR00, GT09} which requ…
A new class of high order semi-Lagrangian schemes for rarefied gas dynamics
Giacomo Dimarco, Cory Hauck, Raphaël Loubère
In this paper we genealize the fast semi-Lagrangian scheme developed in [J. Comput. Phys., Vol. 255, 2013, pp 680-698] to the case of high order reconstructions of the distribution…