M 614

The mathematical basis for the continuum modeling of plasma physics systems is the solution of the governing partial differential equations (PDEs) describing conservation of mass, momentum, and energy, along with various forms of approximations to Maxwell's equations. This PDE system is non-self adjoint, strongly-coupled, highly-nonlinear, and characterized by physical phenomena that span a very large range of length- and time-scales. To enable accurate and stable approximation of these systems a range of spatial and temporal discretization methods are commonly employed. In the context of finite element spatial discretization methods these include mixed integration, stabilized methods and structure-preserving (physics compatible) approaches. For effective time integration for these systems some form of implicitness is required. To enable robust, scalable and efficient solution of the large-scale sparse linear systems gen- erated by the Newton linearization, fully-coupled multilevel preconditioners are developed. The multilevel preconditioners are based on two differing approaches. The first technique employs a graph-based aggregation method applied to the nonzero block structure of the Jacobian matrix. The second approach utilizes approximate block factorization (ABF) methods and physics-based preconditioning approaches that reduce the coupled systems into a set of simplified systems to which multilevel methods are applied. A critical aspect of these methods is the development of approximate Schur complement operators that encode the critical cross-coupling physics of the sys- tem. To demonstrate the exibility and performance of these methods we consider application of these techniques to various forms of resistive MHD models and recent developments for multi uid electromagnetic plasmas. In this context robustness, efficiency, and the parallel and algorithmic scaling of the preconditioning methods are discussed. These results include weak-scaling studies on up to 512K cores. (This is joint work with Edward Phillips, Eric Cyr, Roger Pawlowski, Ray Tuminaro, Paul Lin, and Luis Chacon.) #This work was supported by the DOE office of Science Advanced Scientific Computing Research - Applied Math Research program at Sandia National Laboratory.

Dr. John N. Shadid