Robust and Scalable Solution Methods for Transport/Reaction and Plasma/MHD Simulations

J. N. Shadid, R. P. Pawlowski, J. W. Banks, P. T. Lin, R. S. Tuminaro, P. B. Bochev

Project Goals/Objectives

• Develop stable, accurate, physics compatible, computational formulations for large-scale simulation of Transport/Rx (TR) and Plasma / MHD systems (e.g. Cray XT3 12.5K nodes, 25K cores)
• Develop new robust, efficient and scalable parallel implicit solution methods for multi-physics systems.
• Produce comprehensive accuracy, convergence, stability and scalability studies employing challenging large-scale problems

Approach

• Implicit Methods for multi-time-scale effects
• Physics compatible spatial discretizations
• Robust fully coupled preconditioned Newton-Krylov nonlinear solvers
• Physics-based preconditioners   based on approximate block factorization
• Mulit-level block solvers for scalability (e.g. Drift Diffusion system 10x improvement)

Relevance

• TR and Plasma/MHD critical in science and technology applications for ASCR DOE-SC and SNL (e.g. fusion reactors, astrophysics, materials processing, combustion, fuel cells, alternate and renewable energy, etc.) 
• Development and demonstration of scalable solution methods for PetaScale machines
• Delivering general purpose parallel solution methods in Trilinos packages (NOX, ML, Meros)

Accomplishments

• Developed new implicit stabilized FE formulations for resistive MHD
• Demonstrated initial parallel large-scale bifurcation studies for Hydro-magnetic thermal-convection problems (e.g. relevant to Geo-Dynamo)

• Beginning scalability studies for N-K based solvers with multi-level block preconditioning for resistive MHD

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