Showing 60 results for Author: Cory D. Hauck
Dec, 2022
Journal
The discrete ordinates discontinuous Galerkin (SN-DG) method is a well-established and practical approach for solving the radiative transport equation. In this paper, we study a low-memory variation of the upwind SN-DG method. The proposed method uses a smaller finite element space that is constructed by coupling spatial unknowns across collocation angles, thereby yielding…
Feb, 2022
Conference Paper
The spherical harmonic equations for radiative transport are a linear, hyperbolic set of balance laws that describe the state of a system of particles as they advect through and collide with a material medium. For regimes in which the collisionality of the system is light to moderate, significant qualitative differences have been observed between solutions, based on whethe…
Jan, 2022
Journal
In this paper, properties of a recently proposed mathematical model for data flow in large-scale asynchronous computer systems are analyzed. In particular, the existence of special weak solutions based on propagating fronts is established. Qualitative properties of these solutions are investigated, both theoretically and numerically.
Jan, 2022
Journal
We present an error analysis for the discontinuous Galerkin (DG) method applied to the discrete-ordinate discretization of the steady-state radiative transfer equation with isotropic scattering. Under some mild assumptions, we show that the DG method converges uniformly with respect to a scaling parameter which characterizes the strength of scattering in the system. Howeve…
Aug, 2019
Journal
We show the convergence of the zero relaxation limit of $2 times 2$ systems of hyperbolic balance laws with stochastic initial data. Precisely, solutions converge to a solution of the local equilibrium approximation as the relaxation time tends to zero. The initial data are assumed to depend on finitely many random variables, and the convergence is then proved via the appr…