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On the performance of Krylov smoothing for fully coupled AMG preconditioners for VMS resistive MHD
Author(s) -
Lin Paul T.,
Shadid John N.,
Tsuji Paul H.
Publication year - 2019
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6178
Subject(s) - preconditioner , generalized minimal residual method , multigrid method , domain decomposition methods , solver , mathematics , linear system , context (archaeology) , computer science , computational science , finite element method , iterative method , mathematical optimization , parallel computing , algorithm , partial differential equation , mathematical analysis , physics , paleontology , biology , thermodynamics
Summary This study explores the performance and scaling of a GMRES Krylov method employed as a smoother for an algebraic multigrid preconditioned Newton‐Krylov solution approach applied to a fully implicit variational multiscale finite element resistive magnetohydrodynamics formulation. In this context, a Newton iteration is used for the nonlinear system and a parallel MPI‐based Krylov method is employed for the linear subsystems. The efficiency of this approach is critically dependent on the scalability and performance of the parallel algebraic multigrid preconditioner for the linear solutions and the performance of the multigrid smoothers play a critical role. Krylov multigrid smoothers are considered in an attempt to reduce the time and memory requirements of existing robust smoothers based on additive Schwarz domain decomposition with incomplete LU factorization solves on each subdomain. Three time‐dependent resistive magnetohydrodynamics test cases are considered to evaluate the method. Compared with a domain decomposition incomplete LU smoother, the GMRES smoother can reduce the solve time due to a significant decrease in the preconditioner setup time and often a reduction in outer Krylov solver iterations, and requires less memory, typically 35% less memory.