Krylov Smoothing for Fully-Coupled AMG Preconditioners for VMS Resistive MHD

  • Paul T. LinEmail author
  • John N. Shadid
  • Paul H. Tsuji
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 132)


This study explores the use of a Krylov iterative method (GMRES) as a smoother for an algebraic multigrid (AMG) preconditioned Newton–Krylov iterative solution approach for a fully-implicit variational multiscale (VMS) finite element (FE) resistive magnetohydrodynamics (MHD) formulation. 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 an essential role. Krylov smoothers are considered 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. This brief study presents three time dependent resistive MHD test cases 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.


Multigrid Krylov smoother Preconditioner Newton–Krylov Finite element method Magnetohydrodynamics 



The authors would like to thank R. Pawlowski and E. Cyr for their collaborative effort in developing the Drekar MHD code and D. Sondak and T. Smith for the collaborative development of the VMS LES turbulent MHD modeling capability. The authors gratefully acknowledge the generous support of the DOE NNSA ASC program and the DOE Office of Science AMR program at Sandia National Laboratories. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy, National Nuclear Security Administration under contract DE-NA-0003525.


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Sandia National LaboratoriesAlbuquerqueUSA
  2. 2.Center for Computing ResearchSandia National LaboratoriesAlbuquerqueUSA
  3. 3.Lawrence Livermore National LaboratoryLivermoreUSA

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