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

Abstract

This brief paper explores the development of scalable, nonlinear, fully-implicit 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 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 (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 large-scale sparse linear systems generated by the Newton linearization. We present results for the fully-coupled AMG preconditioner for two prototype problems, a low Lundquist number MHD Faraday conduction pump and moderately-high Lundquist number incompressible magnetic island coalescence problem. For the MHD pump results we explore the scaling of the fully-coupled 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:
; ; ;  [1]; ;
  1. Oak Ridge National Laboratory
Publication Date:
Research Org.:
Sandia National Laboratories
Sponsoring Org.:
USDOE
OSTI Identifier:
1020538
Report Number(s):
SAND2010-3789C
TRN: US201116%%377
DOE Contract Number:  
AC04-94AL85000
Resource Type:
Conference
Resource Relation:
Conference: Proposed for presentation at the European Conference on Computational Fluid Dynamics held June 14-17, 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 fully-coupled 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 fully-coupled 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 fully-coupled AMG and approximate block factorization preconditioners for solution of implicit FE resistive MHD.". United States.
@article{osti_1020538,
title = {Initial performance of fully-coupled 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, fully-implicit 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 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 (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 large-scale sparse linear systems generated by the Newton linearization. We present results for the fully-coupled AMG preconditioner for two prototype problems, a low Lundquist number MHD Faraday conduction pump and moderately-high Lundquist number incompressible magnetic island coalescence problem. For the MHD pump results we explore the scaling of the fully-coupled 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}
}

Conference:
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