57 citations · 131 across the 64 of their papers we have counts for
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An accurate SUPG-stabilized continuous Galerkin discretization for anisotropic heat flux in magnetic confinement fusion
Golo A. Wimmer, Ben S. Southworth, Koki Sagiyama +1
We present a novel spatial discretization for the anisotropic heat conduction equation, aimed at improved accuracy at the high levels of anisotropy seen in a magnetized plasma, for…
Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow
Maria Vasilyeva, Golo A. Wimmer, Ben S. Southworth
We consider anisotropic heat flow with extreme anisotropy, as arises in magnetized plasmas for fusion applications. Such problems pose significant challenges in both obtaining an a…
Physics consistent machine learning framework for inverse modeling with applications to ICF capsule implosions
Daniel A. Serino, Evan Bell, Marc Klasky +4
In high energy density physics (HEDP) and inertial confinement fusion (ICF), predictive modeling is complicated by uncertainty in parameters that characterize various aspects of th…
An adaptive two-grid preconditioner and linearly implicit scheme for shale gas transport in fractured porous media
Maria Vasilyeva, Ben S. Southworth, Shubin Fu
We consider a nonlinear mixed-dimensional model for simulating gas transport in shale formation. The mathematical model consists of a coupled system of nonlinear equations, where f…
Galerkin Formulation of Path Integrals in Lattice Field Theory
Brian K. Tran, Ben S. Southworth
We present a mathematical framework for Galerkin formulations of path integrals in lattice field theory. The framework is based on using the degrees of freedom associated to a Gale…
A structure-preserving discontinuous Galerkin scheme for the Cahn-Hilliard equation including time adaptivity
Golo A. Wimmer, Ben S. Southworth, Qi Tang
We present a novel spatial discretization for the Cahn-Hilliard equation including transport. The method is given by a mixed discretization for the two elliptic operators, with the…
A Geometric Perspective on Kinetic Matter-Radiation Interaction and Moment Systems
Brian K. Tran, Joshua W. Burby, Ben S. Southworth
We provide a geometric perspective on the kinetic interaction of matter and radiation, based on a pair bracket approach. We discuss the interaction of kinetic theories via dissipat…
Consistent Second Moment Methods with Scalable Linear Solvers for Radiation Transport
Samuel Olivier, Ben S. Southworth, James S. Warsa +1
Second Moment Methods (SMMs) are developed that are consistent with the Discontinuous Galerkin (DG) spatial discretization of the discrete ordinates (or \Sn) transport equations. T…
On Properties of Adjoint Systems for Evolutionary PDEs
Brian K. Tran, Ben S. Southworth, Melvin Leok
We investigate the geometric structure of adjoint systems associated with evolutionary partial differential equations at the fully continuous, semi-discrete, and fully discrete lev…
Order Conditions for Nonlinearly Partitioned Runge-Kutta Methods
Brian K. Tran, Ben S. Southworth, Tommaso Buvoli
Recently a new class of nonlinearly partitioned Runge--Kutta (NPRK) methods was proposed for nonlinearly partitioned systems of autonomous ordinary differential equations, $y' = F(…
Generalized Optimal AMG Convergence Theory for Nonsymmetric and Indefinite Problems
Ahsan Ali, James Brannick, Karsten Kahl +3
Algebraic multigrid (AMG) is known to be an effective solver for many sparse symmetric positive definite (SPD) linear systems. For SPD systems, the convergence theory of AMG is wel…
A New Class of Runge-Kutta Methods for Nonlinearly Partitioned Systems
Tommaso Buvoli, Ben S. Southworth
This work introduces a new class of Runge-Kutta methods for solving nonlinearly partitioned initial value problems. These new methods, named nonlinearly partitioned Runge-Kutta (NP…
One-sweep moment-based semi-implicit-explicit integration for gray thermal radiation transport
Ben S. Southworth, Samuel S. Olivier, HyeongKae Park +1
Thermal radiation transport (TRT) is a time dependent, high dimensional partial integro-differential equation. In practical applications such as inertial confinement fusion, TRT is…