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Title: On performance of Krylov smoothing for fully-coupled AMG preconditioners for VMS resistive MHD

Abstract

Here, this study explores the performance and scaling of a GMRES Krylov method employed as a smoother for an algebraic multigrid (AMG) preconditioned Newton- Krylov solution approach applied to a fully-implicit variational multiscale (VMS) nite element (FE) resistive magnetohydrodynamics (MHD) formulation. In this context a Newton iteration is used for the nonlinear system and a Krylov (GMRES) method is employed for the linear subsystems. The efficiency of this approach is critically dependent on the scalability and performance of the AMG preconditioner for the linear solutions and the performance of the smoothers play a critical role. Krylov smoothers are considered in an attempt to reduce the time and memory requirements of existing robust smoothers based on additive Schwarz domain decomposition (DD) with incomplete LU factorization solves on each subdomain. Three time dependent resistive MHD test cases are considered to evaluate the method. The results demonstrate that the GMRES smoother can be faster due to a decrease in the preconditioner setup time and a reduction in outer GMRESR solver iterations, and requires less memory (typically 35% less memory for global GMRES smoother) than the DD ILU smoother.

Authors:
 [1];  [2];  [3]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Univ. of New Mexico, Albuquerque, NM (United States). Department of Mathematics and Statistics,
  3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC)
OSTI Identifier:
1429689
Report Number(s):
SAND-2017-12423J
658741
DOE Contract Number:  
AC04-94AL85000; NA0003525
Resource Type:
Program Document
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Lin, Paul T., Shadid, John N., and Tsuji, Paul H. On performance of Krylov smoothing for fully-coupled AMG preconditioners for VMS resistive MHD. United States: N. p., 2017. Web.
Lin, Paul T., Shadid, John N., & Tsuji, Paul H. On performance of Krylov smoothing for fully-coupled AMG preconditioners for VMS resistive MHD. United States.
Lin, Paul T., Shadid, John N., and Tsuji, Paul H. Wed . "On performance of Krylov smoothing for fully-coupled AMG preconditioners for VMS resistive MHD". United States. doi:.
@article{osti_1429689,
title = {On performance of Krylov smoothing for fully-coupled AMG preconditioners for VMS resistive MHD},
author = {Lin, Paul T. and Shadid, John N. and Tsuji, Paul H.},
abstractNote = {Here, this study explores the performance and scaling of a GMRES Krylov method employed as a smoother for an algebraic multigrid (AMG) preconditioned Newton- Krylov solution approach applied to a fully-implicit variational multiscale (VMS) nite element (FE) resistive magnetohydrodynamics (MHD) formulation. In this context a Newton iteration is used for the nonlinear system and a Krylov (GMRES) method is employed for the linear subsystems. The efficiency of this approach is critically dependent on the scalability and performance of the AMG preconditioner for the linear solutions and the performance of the smoothers play a critical role. Krylov smoothers are considered in an attempt to reduce the time and memory requirements of existing robust smoothers based on additive Schwarz domain decomposition (DD) with incomplete LU factorization solves on each subdomain. Three time dependent resistive MHD test cases are considered to evaluate the method. The results demonstrate that the GMRES smoother can be faster due to a decrease in the preconditioner setup time and a reduction in outer GMRESR solver iterations, and requires less memory (typically 35% less memory for global GMRES smoother) than the DD ILU smoother.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Wed Nov 01 00:00:00 EDT 2017},
month = {Wed Nov 01 00:00:00 EDT 2017}
}

Program Document:
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