Initial performance of fullycoupled AMG and approximate block factorization preconditioners for solution of implicit FE resistive MHD.
Abstract
This brief paper explores the development of scalable, nonlinear, fullyimplicit solution methods for a stabilized unstructured finite element (FE) discretization of the 2D incompressible (reduced) resistive MHD system. The discussion considers the stabilized FE formulation in context of a fullyimplicit time integration and directtosteadystate solution capability. The nonlinear solver strategy employs NewtonKrylov methods, which are preconditioned using fullycoupled algebraic multilevel (AMG) techniques and a new approximate block factorization (ABF) preconditioner. The intent of these preconditioners is to enable robust, scalable and efficient solution approaches for the largescale sparse linear systems generated by the Newton linearization. We present results for the fullycoupled AMG preconditioner for two prototype problems, a low Lundquist number MHD Faraday conduction pump and moderatelyhigh Lundquist number incompressible magnetic island coalescence problem. For the MHD pump results we explore the scaling of the fullycoupled AMG preconditioner for up to 4096 processors for problems with up to 64M unknowns on a CrayXT3/4. Using the island coalescence problem we explore the weak scaling of the AMG preconditioner and the influence of the Lundquist number on the iteration count. Finally we present some very recent results for the algorithmic scaling of the ABF preconditioner.
 Authors:

 Oak Ridge National Laboratory
 Publication Date:
 Research Org.:
 Sandia National Laboratories
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1020538
 Report Number(s):
 SAND20103789C
TRN: US201116%%377
 DOE Contract Number:
 AC0494AL85000
 Resource Type:
 Conference
 Resource Relation:
 Conference: Proposed for presentation at the European Conference on Computational Fluid Dynamics held June 1417, 2010 in Lisbon, Portugal.
 Country of Publication:
 United States
 Language:
 English
 Subject:
 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; COALESCENCE; COMPUTERIZED SIMULATION; FACTORIZATION; FLUID MECHANICS; MAGNETIC ISLANDS; PERFORMANCE
Citation Formats
Shadid, John Nicolas, Lin, Paul Tinphone, Pawlowski, Roger Patrick, Chacon, Luis, Cyr, Eric C, and Tuminaro, Raymond Stephen. Initial performance of fullycoupled AMG and approximate block factorization preconditioners for solution of implicit FE resistive MHD.. United States: N. p., 2010.
Web.
Shadid, John Nicolas, Lin, Paul Tinphone, Pawlowski, Roger Patrick, Chacon, Luis, Cyr, Eric C, & Tuminaro, Raymond Stephen. Initial performance of fullycoupled AMG and approximate block factorization preconditioners for solution of implicit FE resistive MHD.. United States.
Shadid, John Nicolas, Lin, Paul Tinphone, Pawlowski, Roger Patrick, Chacon, Luis, Cyr, Eric C, and Tuminaro, Raymond Stephen. Tue .
"Initial performance of fullycoupled AMG and approximate block factorization preconditioners for solution of implicit FE resistive MHD.". United States.
@article{osti_1020538,
title = {Initial performance of fullycoupled AMG and approximate block factorization preconditioners for solution of implicit FE resistive MHD.},
author = {Shadid, John Nicolas and Lin, Paul Tinphone and Pawlowski, Roger Patrick and Chacon, Luis and Cyr, Eric C and Tuminaro, Raymond Stephen},
abstractNote = {This brief paper explores the development of scalable, nonlinear, fullyimplicit solution methods for a stabilized unstructured finite element (FE) discretization of the 2D incompressible (reduced) resistive MHD system. The discussion considers the stabilized FE formulation in context of a fullyimplicit time integration and directtosteadystate solution capability. The nonlinear solver strategy employs NewtonKrylov methods, which are preconditioned using fullycoupled algebraic multilevel (AMG) techniques and a new approximate block factorization (ABF) preconditioner. The intent of these preconditioners is to enable robust, scalable and efficient solution approaches for the largescale sparse linear systems generated by the Newton linearization. We present results for the fullycoupled AMG preconditioner for two prototype problems, a low Lundquist number MHD Faraday conduction pump and moderatelyhigh Lundquist number incompressible magnetic island coalescence problem. For the MHD pump results we explore the scaling of the fullycoupled AMG preconditioner for up to 4096 processors for problems with up to 64M unknowns on a CrayXT3/4. Using the island coalescence problem we explore the weak scaling of the AMG preconditioner and the influence of the Lundquist number on the iteration count. Finally we present some very recent results for the algorithmic scaling of the ABF preconditioner.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2010},
month = {6}
}