(75f) Progress On a Fully-Implicit Stabilized Finite Element Formulation for Resistive Magnetohydrodynamic Systems

Plasma systems with strong electro-magnetic effects and chemical species transport and reaction occur frequently in nature and are critical for many important technological applications. Examples include stellar interiors, gaseous nebula, the earth's magnetoshpere, and Tokamak and Z-pinch physics. These systems are described by a set of partial differential equations that conserve momentum, mass, charge, and energy for chemical species along with Maxwell's equations for the electric and magnetic fields. The resulting equations are strongly coupled, highly nonlinear, and span a large range of time and length scales, making the scalable, robust, and accurate solution of such systems extremely challenging.

This talk presents the results from an initial study that is intended to explore the development of a scalable fully-implicit stabilized unstructured finite element (FE) capability for low-Mach-number resistive MHD. The brief discussion considers the development of the stabilized FE formulation and the underlying fully-coupled preconditioned Newton-Krylov nonlinear iterative solver. To enable robust, scalable and efficient solution of the large-scale sparse linear systems generated by the Newton linearization, fully-coupled multilevel preconditioners are employed. Parallel performance results are presented for a set of challenging prototype problems that include the solution of an MHD Faraday conduction pump, a hydromagnetic Rayleigh-Bernard linear stability calculation, and a magnetic island coalescence problem. Initial results that explore the scaling of the solution methods are presented on up to 4096 processors for problems with up to 64M unknowns on a CrayXT3/4. Additionally, a large-scale proof-of-capability calculation for 1 billion unknowns for the MHD Faraday pump problem on 24,000 cores is also presented. Finally, the initial results of a Tokamak simulation based on the Solov'ev equilibrium problem will be presented.

*This work was partially funded by the DOE Office of Science AMR Program, and was carried out at Sandia National Laboratories operated for the U.S. Department of Energy under contract no. DE-ACO4-94AL85000