26 citations · 99 across the 14 of their papers we have counts for
16 papers
Structure-preserving finite-element approximations of the magnetic Euler-Poisson equations
Jordan Hoffart, Matthias Maier, John N. Shadid +1
We develop a structure-preserving numerical discretization for the electrostatic Euler-Poisson equations with a given magnetic field. Our focus is on the efficient solution of prob…
Unified -HDG Frameworks for Friedrichs' PDE systems
Jau-Uei Chen, Shinhoo Kang, Tan Bui-Thanh +1
This work proposes a unified -adaptivity framework for hybridized discontinuous Galerkin (HDG) method for a large class of partial differential equations (PDEs) of Friedrichs'…
Structure-preserving finite-element schemes for the Euler-Poisson equations
Matthias Maier, John N. Shadid, Ignacio Tomas
We discuss structure-preserving numerical discretizations for repulsive and attractive Euler-Poisson equations that find applications in fluid-plasma and self-gravitation modeling.…
An adaptive scalable fully implicit algorithm based on stabilized finite element for reduced visco-resistive MHD
Qi Tang, Luis Chacon, Tzanio V. Kolev +2
The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tok…
A Monolithic Algebraic Multigrid Framework for Multiphysics Applications with Examples from Resistive MHD
Peter Ohm, Tobias Wiesner, Eric C. Cyr +3
A multigrid framework is described for multiphysics applications. The framework allows one to construct, adapt, and tailor a monolithic multigrid methodology to different linear sy…
A Multilevel Block Preconditioner for the HDG Trace System Applied to Incompressible Resistive MHD
Sriramkrishnan Muralikrishnan, Stephen Shannon, Tan Bui-Thanh +1
We present a scalable block preconditioning strategy for the trace system coming from the high-order hybridized discontinuous Galerkin (HDG) discretization of incompressible resist…
High Rayleigh number variational multiscale large eddy simulations of Rayleigh-Bénard Convection
David Sondak, Thomas M. Smith, Roger P. Pawlowski +2
The variational multiscale (VMS) formulation is used to develop residual-based VMS large eddy simulation (LES) models for Rayleigh-Bénard convection. The resulting model is a mixed…
An a posteriori error analysis for the equations of stationary incompressible magnetohydrodynamics
J. H. Chaudhry, A. E. Rappaport, J. N. Shadid
Magnetohydrodynamics (MHD) is a continuum level model for conducting fluids subject to external magnetic fields, e.g. plasmas and liquid metals. The efficient and robust solution o…
On differentiable local bounds preserving stabilization for Euler equations
Santiago Badia, Jesús Bonilla, Sibusiso Mabuza +1
This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integr…
A Multilevel Approach for Trace System in HDG Discretizations
Sriramkrishnan Muralikrishnan, Tan Bui-Thanh, John N. Shadid
We propose a multilevel approach for trace systems resulting from hybridized discontinuous Galerkin (HDG) methods. The key is to blend ideas from nested dissection, domain decompos…
Embedded error estimation and adaptive step-size control for optimal explicit strong stability preserving Runge--Kutta methods
Sidafa Conde, Imre Fekete, John N. Shadid
We construct a family of embedded pairs for optimal strong stability preserving explicit Runge-Kutta methods of order to be used to obtain numerical solution of s…
Implicit and Implicit-Explicit Strong Stability Preserving Runge-Kutta Methods with High Linear Order
Sidafa Conde, Sigal Gottlieb, Zachary J. Grant +1
When evolving in time the solution of a hyperbolic partial differential equation, it is often desirable to use high order strong stability preserving (SSP) time discretizations. Th…
Analysis of an HDG Method for Linearized Incompressible Resistive MHD Equations
Jeonghun J. Lee, Stephen Shannon, Tan Bui-Thanh +1
We present a hybridized discontinuous Galerkin (HDG) method for stationary linearized incompressible magnetohydrodynamics (MHD) equations. At the heart of the paper is the introduc…
Dimension reduction in MHD power generation models: dimensional analysis and active subspaces
Andrew Glaws, Paul G. Constantine, John Shadid +1
Magnetohydrodynamics (MHD)---the study of electrically conducting fluids---can be harnessed to produce efficient, low-emissions power generation. Today, computational modeling assi…
Error Estimation for Multi-Stage Runge-Kutta IMEX Schemes
Jehanzeb H. Chaudhry, J. B. Collins, John N. Shadid
Implicit-Explicit (IMEX) schemes are widely used for time integration methods for approximating solutions to a large class of problems. In this work, we develop accurate a posterio…
A new class of finite element variational multiscale turbulence models for incompressible magnetohydrodynamics
David Sondak, John N. Shadid, Assad A. Oberai +3
New large eddy simulation (LES) turbulence models for incompressible magnetohydrodynamics (MHD) derived from the variational multiscale (VMS) formulation for finite element simulat…