J.N. Shadid, E.C. Cyr, R.P. Pawlowski, R.S. Tuminaro, L. Chacon, and P.T. Lin,
Initial Performance of Fully-Coupled AMG and Approximate Block
Factorization Preconditioners for Solution of Implicit FE Resitive MHD,
Proceedings of ECCOMAS-CFD 2010,
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.
Contact Eric Cyr for a copy