57 citations · 131 across the 64 of their papers we have counts for
49 papers · 1 filter
An Efficient Solver for Finite Element-based Constrained Transport in 3D Magnetohydrodynamics Applied to Magnetic Confinement Fusion
Golo A. Wimmer, Konstantin Lipnikov, Ben S. Southworth +1
We present an efficient solver framework for the stiff magnetic wave coupling arising in resistive magnetohydrodynamics (MHD) on realistic tokamak geometries. The approach builds o…
Broken-space Additive Schwarz Mass Inverse Approximations and (Block) Preconditioning
Oliver A. Krzysik, Ben S. Southworth, Golo A. Wimmer
Finite-element mass matrix solves and approximate inverses arise often in explicit time integration as well as Schur-complement-based block preconditioning. A diagonal approximatio…
A black-box, multilevel algebraic preconditioning framework for conforming finite elements
O. A. Krzysik, B. S. Southworth, G. A. Wimmer
Recently we introduced the least-squares algebraic-multigrid domain-decomposition (LS-AMG-DD) method as a multilevel, algebraic preconditioner for sparse symmetric positive definit…
Two-level convergence of Algebraic Multigrid with Overlapping Smoothers and Spectral Coarse Grids
O. A. Krzysik, B. S. Southworth, H. Al Daas
We recently developed the least-squares algebraic-multigrid domain-decomposition (LS-AMG-DD) solver as an algebraic multilevel method for sparse symmetric positive definite matrice…
Algebraic Multigrid with Overlapping Schwarz Smoothers and Local Spectral Coarse Grids for Least Squares Problems
Ben S. Southworth, Hussam Al Daas, Golo A. Wimmer +1
This paper develops a new algebraic multigrid (AMG) method for sparse least-squares systems of the form motivated by challenging applications in scientific computing where…
Preconditioning a hybridizable discontinuous Galerkin method for Navier-Stokes at high Reynolds number
Alexander D. Lindsay, Sander Rhebergen, Ben S. Southworth
We introduce a preconditioner for a hybridizable discontinuous Galerkin discretization of the linearized Navier-Stokes equations at high Reynolds number. The preconditioner is base…
Multiscale Graph Reduction for Heterogeneous and Anisotropic Discrete Diffusion Processes
Maria Vasilyeva, James Brannick, Ben S. Southworth
We present multiscale graph-based reduction algorithms for upscaling heterogeneous and anisotropic diffusion problems. The proposed coarsening approaches begin by constructing a pa…
Implicit-Explicit Scheme with Multiscale Vanka Two-Grid Solver for Heterogeneous Unsaturated Poroelasticity
Maria Vasilyeva, Ben S. Southworth, Yunhui He +1
We consider a coupled nonlinear system of equations that describe unsaturated flow in heterogeneous poroelastic media. For the numerical solution, we use a finite element approxima…
Optimal transfer operators in algebraic two-level methods for nonsymmetric and indefinite problems
Oliver A. Krzysik, Ben S. Southworth, Golo A. Wimmer +3
Consider an algebraic two-level method applied to the -dimensional linear system using fine-space preconditioner (i.e., ``relaxation'' or ``smoother'…
Multirate Runge-Kutta for Nonlinearly Partitioned Systems
Tommaso Buvoli, Brian K. Tran, Ben S. Southworth
Multirate integration is an increasingly relevant tool that enables scientists to simulate multiphysics systems. Existing multirate methods are designed for equations whose fast an…
Generalized Optimal AMG Convergence Theory for Stokes Equations Using Smooth Aggregation and Vanka Relaxation Strategies
Ahsan Ali, James J. Brannick, Karsten Kahl +4
This paper discusses our recent generalized optimal algebraic multigrid (AMG) convergence theory applied to the steady-state Stokes equations discretized using Taylor-Hood elements…
Moment-based adaptive time integration for thermal radiation transport
Ben S. Southworth, Steven Walton, Steven B. Roberts +1
In this paper we develop a framework for moment-based adaptive time integration of deterministic multifrequency thermal radiation transpot (TRT). We generalize our recent semi-impl…
Overlapping Schwarz methods are not anisotropy-robust multigrid smoothers
Oliver A. Krzysik, Ben S. Southworth, Bobby Philip
We analyze overlapping multiplicative Schwarz methods as smoothers in the geometric multigrid solution of two-dimensional anisotropic diffusion problems. For diffusion equations, i…
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…
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…
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…
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…
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…
Space-Time Block Preconditioning for Incompressible Resistive Magnetohydrodynamics
Federico Danieli, Ben S. Southworth, Jacob B. Schroder
This work develops an all-at-once space-time preconditioning approach for resistive magnetohydrodynamics (MHD). We consider parallel-in-time due to the long time domains required t…
On Compatible Transfer Operators in Nonsymmetric Algebraic Multigrid
Ben S. Southworth, Thomas A. Manteuffel
The standard goal for an effective algebraic multigrid (AMG) algorithm is to develop relaxation and coarse-grid correction schemes that attenuate complementary error modes. In the…