Solution of the implicitly discretised fluid flow equations by operator-splitting
Journal of Computational Physics
Computer Methods in Applied Mechanics and Engineering
Computer Methods in Applied Mechanics and Engineering
Semi-implicit magnetohydrodynamic calculations
Journal of Computational Physics
Finite element analysis of the compressible Euler and Navier-Stokes equations
Finite element analysis of the compressible Euler and Navier-Stokes equations
Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
An analysis of the fractional step method
Journal of Computational Physics
Iterative solution methods
Choosing the forcing terms in an inexact Newton method
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
A simple finite difference scheme for multidimensional magnetohydrodynamical equations
Journal of Computational Physics
The Accuracy of the Fractional Step Method
SIAM Journal on Numerical Analysis
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
Parallel multilevel k-way partitioning scheme for irregular graphs
Supercomputing '96 Proceedings of the 1996 ACM/IEEE conference on Supercomputing
Multigrid
Divergence-free adaptive mesh refinement for Magnetohydrodynamics
Journal of Computational Physics
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Hyperbolic divergence cleaning for the MHD equations
Journal of Computational Physics
An implicit, nonlinear reduced resistive MHD solver
Journal of Computational Physics
On balanced approximations for time integration of multiple time scale systems
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A 2D high-ß Hall MHD implicit nonlinear solver
Journal of Computational Physics
A Taxonomy of Consistently Stabilized Finite Element Methods for the Stokes Problem
SIAM Journal on Scientific Computing
Nonlinear magnetohydrodynamics simulation using high-order finite elements
Journal of Computational Physics
Journal of Computational Physics
An overview of the Trilinos project
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
An Improved Convergence Bound for Aggregation-Based Domain Decomposition Preconditioners
SIAM Journal on Matrix Analysis and Applications
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
A fully implicit numerical method for single-fluid resistive magnetohydrodynamics
Journal of Computational Physics
An adaptive finite element method for magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
A New Petrov-Galerkin Smoothed Aggregation Preconditioner for Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
Journal of Computational Physics
Accurate semi-implicit treatment of the Hall effect in magnetohydrodynamic computations
Journal of Computational Physics
Operator-Based Preconditioning of Stiff Hyperbolic Systems
SIAM Journal on Scientific Computing
Journal of Computational Physics
Approximation of the inductionless MHD problem using a stabilized finite element method
Journal of Computational Physics
Stabilization and scalable block preconditioning for the Navier-Stokes equations
Journal of Computational Physics
Review of implicit methods for the magnetohydrodynamic description of magnetically confined plasmas
Journal of Computational Physics
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational Physics
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
International Journal of High Performance Computing Applications
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This paper explores the development of a scalable, nonlinear, fully-implicit stabilized unstructured finite element (FE) capability for 2D incompressible (reduced) resistive MHD. The discussion considers the implementation of a stabilized FE formulation in context of a fully-implicit time integration and direct-to-steady-state solution capability. The nonlinear solver strategy employs Newton-Krylov methods, which are preconditioned using fully-coupled algebraic multilevel preconditioners. These preconditioners are shown to enable a robust, scalable and efficient solution approach for the large-scale sparse linear systems generated by the Newton linearization. Verification results demonstrate the expected order-of-accuracy for the stabilized FE discretization. The approach is tested on a variety of prototype problems, including both low-Lundquist number (e.g., an MHD Faraday conduction pump and a hydromagnetic Rayleigh-Bernard linear stability calculation) and moderately-high Lundquist number (magnetic island coalescence problem) examples. Initial results that explore the scaling of the solution methods are presented on up to 4096 processors for problems with up to 64M unknowns on a CrayXT3/4. Additionally, a large-scale proof-of-capability calculation for 1 billion unknowns for the MHD Faraday pump problem on 24,000 cores is presented.