Scalable Multiphysics Block Preconditioning for Low Mach Number Compressible Resistive MHD with Application to Magnetic Confinement Fusion

Ohm, Peter; Bonilla de Toro, Jesus; Phillips, Edward; Shadid, John N.; Crockatt, Michael M.; Tuminaro, Raymond S.; Hu, Jonathan J.; Tang, Xian-Zhu

doi:10.1137/23m1582667

Scalable Multiphysics Block Preconditioning for Low Mach Number Compressible Resistive MHD with Application to Magnetic Confinement Fusion

Journal Article · Fri Jul 05 00:00:00 EDT 2024 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/23m1582667· OSTI ID:2478091

^[1]; ^[2]; Phillips, Edward ^[3]; Shadid, John N. ^[4]; Crockatt, Michael M. ^[3]; Tuminaro, Raymond S. ^[5]; ^[5]; ^[2]

RIKEN Center for Computational Science, Kobe (Japan)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); University of New Mexico, Albuquerque, NM (United States)
Sandia National Laboratories (SNL-CA), Livermore, CA (United States)

This study investigates multiphysics block preconditioners that are critical in devising scalable Newton–Krylov iterative solvers for longer time-scale fully implicit fluid plasma models. The specific model of interest is the visco-resistive, low Mach number, compressible magnetohydrodynamics (MHD) model. This model describes the dynamics of conducting fluids in the presence of electromagnetic fields and can be used to study aspects of astrophysical phenomena, important science and technology applications, and basic plasma physics. The specific application of interest that motivates this study is the macroscopic simulation of longer time-scale stability and disruptions of magnetic confinement fusion devices, specifically the ITER Tokamak. The computational solution of the governing balance equations for mass, momentum, heat transfer, and magnetic induction for resistive MHD systems can be extremely challenging. These difficulties arise from both the strong nonlinear, nonsymmetric coupling of fluid and electromagnetic phenomena as well as the significant range of time and length scales that the interactions of these physical mechanisms produce. To handle the range of time and spatial scales of interest, a fully implicit unstructured variational multiscale finite element formulation is employed. For the scalable solution of the Newton linearized systems, fully coupled block preconditioners are designed to leverage algebraic multigrid subsolves. In conclusion, results are presented for the strong and weak scaling of the method as well as the robustness of these techniques for a large range of Lundquist numbers.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC); USDOE Office of Science (SC), Fusion Energy Sciences (FES)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 2478091

Report Number(s):: LA-UR--23-33406

Journal Information:: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 5 Vol. 46; ISSN 1064-8275

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

References (81)

A parallel fully coupled algebraic multilevel preconditioner applied to multiphysics PDE applications: Drift-diffusion, flow/transport/reaction, resistive MHD Lin, Paul T.; Shadid, John N.; Tuminaro, Raymond S. International Journal for Numerical Methods in Fluids, Vol. 64, Issue 10-12 https://doi.org/10.1002/fld.2402	journal	September 2010
An algebraic multigrid method for Q ₂ − Q ₁ mixed discretizations of the Navier-Stokes equations: AMG for Q ₂ − Q ₁ discretization Prokopenko, Andrey; Tuminaro, Raymond S. Numerical Linear Algebra with Applications, Vol. 24, Issue 6 https://doi.org/10.1002/nla.2109	journal	June 2017
A local Fourier analysis of additive Vanka relaxation for the Stokes equations Farrell, Patrick E.; He, Yunhui; MacLachlan, Scott P. Numerical Linear Algebra with Applications, Vol. 28, Issue 3 https://doi.org/10.1002/nla.2306	journal	June 2020
Toward efficient polynomial preconditioning for GMRES Loe, Jennifer A.; Morgan, Ronald B. Numerical Linear Algebra with Applications, Vol. 29, Issue 4 https://doi.org/10.1002/nla.2427	journal	December 2021
A general approach to analyse preconditioners for two‐by‐two block matrices Axelsson, Owe; Neytcheva, Maya Numerical Linear Algebra with Applications, Vol. 20, Issue 5 https://doi.org/10.1002/nla.830	journal	December 2011
Performance of a Petrov–Galerkin algebraic multilevel preconditioner for finite element modeling of the semiconductor device drift‐diffusion equations Lin, Paul T.; Shadid, John N.; Tuminaro, Ray S. International Journal for Numerical Methods in Engineering, Vol. 84, Issue 4 https://doi.org/10.1002/nme.2902	journal	April 2010
Hyperbolic Divergence Cleaning for the MHD Equations Dedner, A.; Kemm, F.; Kröner, D. Journal of Computational Physics, Vol. 175, Issue 2 https://doi.org/10.1006/jcph.2001.6961	journal	January 2002
An Implicit, Nonlinear Reduced Resistive MHD Solver Chacón, L.; Knoll, D. A.; Finn, J. M. Journal of Computational Physics, Vol. 178, Issue 1 https://doi.org/10.1006/jcph.2002.7015	journal	May 2002
Krylov Smoothing for Fully-Coupled AMG Preconditioners for VMS Resistive MHD Lin, Paul T.; Shadid, John N.; Tsuji, Paul H. Lecture Notes in Computational Science and Engineering https://doi.org/10.1007/978-3-030-30705-9_24	book	January 2020
Numerical Methods for Gasdynamic Systems on Unstructured Meshes Barth, Timothy J. An Introduction to Recent Developments in Theory and Numerics for Conservation Laws https://doi.org/10.1007/978-3-642-58535-7_5	book	January 1999
Convergence of block iterative methods for linear systems arising in the numerical solution of Euler equations Elsner, Ludwig; Mehrmann, Volker Numerische Mathematik, Vol. 59, Issue 1 https://doi.org/10.1007/BF01385795	journal	December 1991
Coupled algebraic multigrid methods for the Oseen problem Wabro, Markus Computing and Visualization in Science, Vol. 7, Issue 3-4 https://doi.org/10.1007/s00791-004-0138-z	journal	October 2004
Smoothed aggregation multigrid for a Stokes problem Janka, Aleš Computing and Visualization in Science, Vol. 11, Issue 3 https://doi.org/10.1007/s00791-007-0068-7	journal	February 2007
Fusion Simulation Project Workshop Report Kritz, Arnold; Keyes, David Journal of Fusion Energy, Vol. 28, Issue 1 https://doi.org/10.1007/s10894-008-9151-4	journal	June 2008
Multigrid Methods for the Stokes Equations using Distributive Gauss–Seidel Relaxations based on the Least Squares Commutator Wang, Ming; Chen, Long Journal of Scientific Computing, Vol. 56, Issue 2 https://doi.org/10.1007/s10915-013-9684-1	journal	February 2013
Block-implicit multigrid solution of Navier-Stokes equations in primitive variables Vanka, S. P. Journal of Computational Physics, Vol. 65, Issue 1 https://doi.org/10.1016/0021-9991(86)90008-2	journal	July 1986
Simulation of runaway electrons during tokamak disruptions Eriksson, L. -G.; Helander, P. Computer Physics Communications, Vol. 154, Issue 3 https://doi.org/10.1016/S0010-4655(03)00293-5	journal	August 2003
A 2D high-β Hall MHD implicit nonlinear solver Chacón, L.; Knoll, D. A. Journal of Computational Physics, Vol. 188, Issue 2 https://doi.org/10.1016/S0021-9991(03)00193-1	journal	July 2003
Lifetime evaluation of plasma-facing materials during a tokamak disruption Hassanein, A.; Konkashbaev, I. Journal of Nuclear Materials, Vol. 233-237 https://doi.org/10.1016/S0022-3115(96)00213-9	journal	October 1996
The variational multiscale method—a paradigm for computational mechanics Hughes, Thomas J. R.; Feijóo, Gonzalo R.; Mazzei, Luca Computer Methods in Applied Mechanics and Engineering, Vol. 166, Issue 1-2 https://doi.org/10.1016/S0045-7825(98)00079-6	journal	November 1998
An efficient smoother for the Stokes problem Braess, D.; Sarazin, R. Applied Numerical Mathematics, Vol. 23, Issue 1 https://doi.org/10.1016/S0168-9274(96)00059-1	journal	February 1997
Performance of fully-coupled algebraic multigrid preconditioners for large-scale VMS resistive MHD Lin, P. T.; Shadid, J. N.; Hu, J. J. Journal of Computational and Applied Mathematics, Vol. 344 https://doi.org/10.1016/j.cam.2017.09.028	journal	December 2018
Large-scale stabilized FE computational analysis of nonlinear steady-state transport/reaction systems Shadid, J. N.; Salinger, A. G.; Pawlowski, R. P. Computer Methods in Applied Mechanics and Engineering, Vol. 195, Issue 13-16 https://doi.org/10.1016/j.cma.2005.05.047	journal	February 2006
Scalable implicit incompressible resistive MHD with stabilized FE and fully-coupled Newton–Krylov-AMG Shadid, J. N.; Pawlowski, R. P.; Cyr, E. C. Computer Methods in Applied Mechanics and Engineering, Vol. 304 https://doi.org/10.1016/j.cma.2016.01.019	journal	June 2016
On a fully-implicit VMS-stabilized FE formulation for low Mach number compressible resistive MHD with application to MCF Bonilla, J.; Shadid, J. N.; Tang, X. -Z. Computer Methods in Applied Mechanics and Engineering, Vol. 417 https://doi.org/10.1016/j.cma.2023.116359	journal	December 2023
An efficient high-order numerical solver for diffusion equations with strong anisotropy Green, David; Hu, Xiaozhe; Lore, Jeremy Computer Physics Communications, Vol. 276 https://doi.org/10.1016/j.cpc.2022.108333	journal	July 2022
Jacobian-free Newton–Krylov methods: a survey of approaches and applications Knoll, D. A.; Keyes, D. E. Journal of Computational Physics, Vol. 193, Issue 2 https://doi.org/10.1016/j.jcp.2003.08.010	journal	January 2004
Studies of the accuracy of time integration methods for reaction–diffusion equations Ropp, David L.; Shadid, John N.; Ober, Curtis C. Journal of Computational Physics, Vol. 194, Issue 2 https://doi.org/10.1016/j.jcp.2003.08.033	journal	March 2004
Nonlinear magnetohydrodynamics simulation using high-order finite elements Sovinec, C. R.; Glasser, A. H.; Gianakon, T. A. Journal of Computational Physics, Vol. 195, Issue 1 https://doi.org/10.1016/j.jcp.2003.10.004	journal	March 2004
Stability of operator splitting methods for systems with indefinite operators: reaction-diffusion systems Ropp, David L.; Shadid, John N. Journal of Computational Physics, Vol. 203, Issue 2 https://doi.org/10.1016/j.jcp.2004.09.004	journal	March 2005
Performance of fully coupled domain decomposition preconditioners for finite element transport/reaction simulations Shadid, J. N.; Tuminaro, R. S.; Devine, K. D. Journal of Computational Physics, Vol. 205, Issue 1 https://doi.org/10.1016/j.jcp.2004.10.038	journal	May 2005
Finite element and higher order difference formulations for modelling heat transport in magnetised plasmas Günter, S.; Lackner, K.; Tichmann, C. Journal of Computational Physics, Vol. 226, Issue 2 https://doi.org/10.1016/j.jcp.2007.07.016	journal	October 2007
A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier–Stokes equations Elman, Howard; Howle, V. E.; Shadid, John Journal of Computational Physics, Vol. 227, Issue 3 https://doi.org/10.1016/j.jcp.2007.09.026	journal	January 2008
Stability of operator splitting methods for systems with indefinite operators: Advection–diffusion–reaction systems Ropp, David L.; Shadid, John N. Journal of Computational Physics, Vol. 228, Issue 9 https://doi.org/10.1016/j.jcp.2009.02.001	journal	May 2009
Performance of a parallel algebraic multilevel preconditioner for stabilized finite element semiconductor device modeling Lin, Paul T.; Shadid, John N.; Sala, Marzio Journal of Computational Physics, Vol. 228, Issue 17 https://doi.org/10.1016/j.jcp.2009.05.024	journal	September 2009
Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods Shadid, J. N.; Pawlowski, R. P.; Banks, J. W. Journal of Computational Physics, Vol. 229, Issue 20 https://doi.org/10.1016/j.jcp.2010.06.018	journal	October 2010
Review of implicit methods for the magnetohydrodynamic description of magnetically confined plasmas Jardin, S. C. Journal of Computational Physics, Vol. 231, Issue 3 https://doi.org/10.1016/j.jcp.2010.12.025	journal	February 2012
An asymptotic-preserving semi-Lagrangian algorithm for the time-dependent anisotropic heat transport equation Chacón, L.; del-Castillo-Negrete, D.; Hauck, C. D. Journal of Computational Physics, Vol. 272 https://doi.org/10.1016/j.jcp.2014.04.049	journal	September 2014
A scalable, fully implicit algorithm for the reduced two-field low-β extended MHD model Chacón, L.; Stanier, A. Journal of Computational Physics, Vol. 326 https://doi.org/10.1016/j.jcp.2016.09.007	journal	December 2016
A robust solver for the finite element approximation of stationary incompressible MHD equations in 3D Li, Lingxiao; Zheng, Weiying Journal of Computational Physics, Vol. 351 https://doi.org/10.1016/j.jcp.2017.09.025	journal	December 2017
IMEX and exact sequence discretization of the multi-fluid plasma model Miller, S. T.; Cyr, E. C.; Shadid, J. N. Journal of Computational Physics, Vol. 397 https://doi.org/10.1016/j.jcp.2019.05.052	journal	November 2019
Disruptions in ITER and strategies for their control and mitigation Lehnen, M.; Aleynikova, K.; Aleynikov, P. B. Journal of Nuclear Materials, Vol. 463 https://doi.org/10.1016/j.jnucmat.2014.10.075	journal	August 2015
Principles of Magnetohydrodynamics: With Applications to Laboratory and Astrophysical Plasmas Goedbloed, J. P. Hans; Poedts, Stefaan https://doi.org/10.1017/CBO9780511616945	book	February 2010
Sweet's mechanism for merging magnetic fields in conducting fluids Parker, E. N. Journal of Geophysical Research, Vol. 62, Issue 4 https://doi.org/10.1029/JZ062i004p00509	journal	December 1957
Disruption prediction with artificial intelligence techniques in tokamak plasmas Vega, J.; Murari, A.; Dormido-Canto, S. Nature Physics, Vol. 18, Issue 7 https://doi.org/10.1038/s41567-022-01602-2	journal	June 2022
Measurement of plasma electron temperature and effective charge during tokamak disruptions Whyte, D. G.; Humphreys, D. A.; Taylor, P. L. Physics of Plasmas, Vol. 7, Issue 10 https://doi.org/10.1063/1.1288678	journal	January 2000
An optimal, parallel, fully implicit Newton–Krylov solver for three-dimensional viscoresistive magnetohydrodynamics Chacón, L. Physics of Plasmas, Vol. 15, Issue 5 https://doi.org/10.1063/1.2838244	journal	May 2008
Understanding disruptions in tokamaks Zakharov, Leonid E.; Galkin, Sergei A.; Gerasimov, Sergei N. Physics of Plasmas, Vol. 19, Issue 5 https://doi.org/10.1063/1.4705694	journal	May 2012
Hall effect on tearing mode instabilities in tokamak Zhang, W.; Ma, Z. W.; Wang, S. Physics of Plasmas, Vol. 24, Issue 10 https://doi.org/10.1063/1.5004430	journal	October 2017
3D simulations of vertical displacement events in tokamaks: A benchmark of M3D-C ¹ , NIMROD, and JOREK Artola, F. J.; Sovinec, C. R.; Jardin, S. C. Physics of Plasmas, Vol. 28, Issue 5 https://doi.org/10.1063/5.0037115	journal	May 2021
Progress toward fusion energy breakeven and gain as measured against the Lawson criterion Wurzel, Samuel E.; Hsu, Scott C. Physics of Plasmas, Vol. 29, Issue 6 https://doi.org/10.1063/5.0083990	journal	June 2022
Nonlinear simulation studies of tokamaks and STs Park, W.; Breslau, J.; Chen, J. Nuclear Fusion, Vol. 43, Issue 6 https://doi.org/10.1088/0029-5515/43/6/311	journal	June 2003
Progress in understanding disruptions triggered by massive gas injection via 3D non-linear MHD modelling with JOREK Nardon, E.; Fil, A.; Hoelzl, M. Plasma Physics and Controlled Fusion, Vol. 59, Issue 1 https://doi.org/10.1088/0741-3335/59/1/014006	journal	October 2016
Cross-validation of analytical models for computation of disruption forces in tokamaks Isernia, N.; Pustovitov, V. D.; Villone, F. Plasma Physics and Controlled Fusion, Vol. 61, Issue 11 https://doi.org/10.1088/1361-6587/ab4016	journal	September 2019
Role of Hall effect on the resistive kink mode in tokamaks Zhang, W.; Ma, Z. W.; Zhang, H. W. Plasma Physics and Controlled Fusion, Vol. 62, Issue 2 https://doi.org/10.1088/1361-6587/ab60ff	journal	January 2020
3D two-temperature magnetohydrodynamic modeling of fast thermal quenches due to injected impurities in tokamaks Ferraro, N. M.; Lyons, B. C.; Kim, C. C. Nuclear Fusion, Vol. 59, Issue 1 https://doi.org/10.1088/1741-4326/aae990	journal	November 2018
The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas Hoelzl, Matthias; Huijsmans, Guido; Pamela, Stanislas Nuclear Fusion https://doi.org/10.1088/1741-4326/abf99f	journal	April 2021
Models and scalings for the disruption forces in tokamaks Pustovitov, V. D. Nuclear Fusion, Vol. 62, Issue 2 https://doi.org/10.1088/1741-4326/ac3fe9	journal	January 2022
Scalable parallel implicit solvers for 3D magnetohydrodynamics Chacón, L. Journal of Physics: Conference Series, Vol. 125 https://doi.org/10.1088/1742-6596/125/1/012041	journal	July 2008
Analysis of iterative methods for saddle point problems: a unified approach Zulehner, Walter Mathematics of Computation, Vol. 71, Issue 238 https://doi.org/10.1090/S0025-5718-01-01324-2	journal	May 2001
Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics Elman, Howard; Silvester, David; Wathen, Andy https://doi.org/10.1093/acprof:oso/9780199678792.001.0001	book	May 2014
Block Preconditioners Based on Approximate Commutators Elman, Howard; Howle, Victoria E.; Shadid, John SIAM Journal on Scientific Computing, Vol. 27, Issue 5 https://doi.org/10.1137/040608817	journal	January 2006
AMGe---Coarsening Strategies and Application to the Oseen Equations Wabro, Markus SIAM Journal on Scientific Computing, Vol. 27, Issue 6 https://doi.org/10.1137/040610350	journal	January 2006
Operator-Based Preconditioning of Stiff Hyperbolic Systems Reynolds, Daniel R.; Samtaney, Ravi; Woodward, Carol S. SIAM Journal on Scientific Computing, Vol. 32, Issue 1 https://doi.org/10.1137/080713331	journal	January 2010
Choosing the Forcing Terms in an Inexact Newton Method Eisenstat, Stanley C.; Walker, Homer F. SIAM Journal on Scientific Computing, Vol. 17, Issue 1 https://doi.org/10.1137/0917003	journal	January 1996
Iterative Methods for Sparse Linear Systems Saad, Yousef https://doi.org/10.1137/1.9780898718003	book	January 2003
A Multigrid Tutorial, Second Edition Briggs, William L.; Henson, Van Emden; McCormick, Steve F. Other Titles in Applied Mathematics https://doi.org/10.1137/1.9780898719505	book	January 2000
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations Ascher, Uri M.; Petzold, Linda R. https://doi.org/10.1137/1.9781611971392	book	January 1998
A New Approximate Block Factorization Preconditioner for Two-Dimensional Incompressible (Reduced) Resistive MHD Cyr, Eric C.; Shadid, John N.; Tuminaro, Raymond S. SIAM Journal on Scientific Computing, Vol. 35, Issue 3 https://doi.org/10.1137/12088879X	journal	January 2013
A Block Preconditioner for an Exact Penalty Formulation for Stationary MHD Phillips, Edward G.; Elman, Howard C.; Cyr, Eric C. SIAM Journal on Scientific Computing, Vol. 36, Issue 6 https://doi.org/10.1137/140955082	journal	January 2014
Teko: A Block Preconditioning Capability with Concrete Example Applications in Navier--Stokes and MHD Cyr, Eric C.; Shadid, John N.; Tuminaro, Raymond S. SIAM Journal on Scientific Computing, Vol. 38, Issue 5 https://doi.org/10.1137/15M1017946	journal	January 2016
Block Preconditioners for Stable Mixed Nodal and Edge finite element Representations of Incompressible Resistive MHD Phillips, Edward G.; Shadid, John N.; Cyr, Eric C. SIAM Journal on Scientific Computing, Vol. 38, Issue 6 https://doi.org/10.1137/16M1074084	journal	January 2016
Preconditioners for Mixed Finite Element Discretizations of Incompressible MHD Equations Wathen, Michael; Greif, Chen; Schötzau, Dominik SIAM Journal on Scientific Computing, Vol. 39, Issue 6 https://doi.org/10.1137/16M1098991	journal	January 2017
A Scalable Approximate Inverse Block Preconditioner for an Incompressible Magnetohydrodynamics Model Problem Wathen, Michael; Greif, Chen SIAM Journal on Scientific Computing, Vol. 42, Issue 1 https://doi.org/10.1137/19M1255409	journal	January 2020
Monolithic Multigrid Methods for Magnetohydrodynamics Adler, James H.; Benson, Thomas R.; Cyr, Eric C. SIAM Journal on Scientific Computing, Vol. 43, Issue 5 https://doi.org/10.1137/20M1348364	journal	January 2021
A Parallel Cut-Cell Algorithm for the Free-Boundary Grad--Shafranov Problem Liu, Shuang; Tang, Qi; Tang, Xian-zhu SIAM Journal on Scientific Computing, Vol. 43, Issue 6 https://doi.org/10.1137/20M1385470	journal	January 2021
An Augmented Lagrangian Preconditioner for the Magnetohydrodynamics Equations at High Reynolds and Coupling Numbers Laakmann, Fabian; Farrell, Patrick E.; Mitchell, Lawrence SIAM Journal on Scientific Computing, Vol. 44, Issue 4 https://doi.org/10.1137/21M1416539	journal	August 2022
Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems Bramble, James H.; Pasciak, Joseph E.; Vassilev, Apostol T. SIAM Journal on Numerical Analysis, Vol. 34, Issue 3 https://doi.org/10.1137/S0036142994273343	journal	June 1997
An overview of the Trilinos project Heroux, Michael A.; Phipps, Eric T.; Salinger, Andrew G. ACM Transactions on Mathematical Software, Vol. 31, Issue 3 https://doi.org/10.1145/1089014.1089021	journal	September 2005
Requirements for Triggering the ITER Disruption Mitigation System de Vries, P. C.; Pautasso, G.; Humphreys, D. Fusion Science and Technology, Vol. 69, Issue 2 https://doi.org/10.13182/FST15-176	journal	April 2016
A monolithic algebraic multigrid framework for multiphysics applications with examples from resistive MHD Ohm, Peter; Wiesner, Tobias A.; Cyr, Eric C. ETNA - Electronic Transactions on Numerical Analysis, Vol. 55 https://doi.org/10.1553/etna_vol55s365	journal	January 2022

Similar Records

On a fully-implicit VMS-stabilized FE formulation for low Mach number compressible resistive MHD with application to MCF

Journal Article · Tue Aug 22 20:00:00 EDT 2023 · Computer Methods in Applied Mechanics and Engineering · OSTI ID:1998134

Initial performance of fully-coupled AMG and approximate block factorization preconditioners for solution of implicit FE resistive MHD.

Conference · Tue Jun 01 00:00:00 EDT 2010 · OSTI ID:1020538

Scalable implicit incompressible resistive MHD with stabilized FE and fully-coupled Newton–Krylov-AMG

Journal Article · Tue Feb 09 19:00:00 EST 2016 · Computer Methods in Applied Mechanics and Engineering · OSTI ID:1310309

Related Subjects

97 MATHEMATICS AND COMPUTING
block preconditioning
fully implicit
large-scale parallel
magnetic fusion energy
magnetohydrodynamics
mathematics
multilevel preconditioner
stabilized finite element

Scalable Multiphysics Block Preconditioning for Low Mach Number Compressible Resistive MHD with Application to Magnetic Confinement Fusion

Citation Formats

References (81)

Similar Records

Related Subjects