Scalable Preconditioning of Implicit Resistive MHD Formulations with Application to Magnetic Confinement Fusion (MCF)

Abstract: 

In this talk, Dr. John N. Shadid will present a scalable multiphysics block preconditioner for an implicit low Mach number compressible resistive magnetohydrodynamics (MHD) formulation based on a variational multiscale finite element method.  The solution of the strongly coupled highly nonlinear discretized system is achieved with a fully coupled Newton nonlinear iterative method.  The resulting large-scale sparse linear systems are iteratively solved by a generalized minimal residual Krylov method, preconditioned by approximate block factorization and physics-based preconditioning approaches.  These methods reduce the coupled multiphysics system to a set of simplified sub-systems to which scalable algebraic multilevel methods can be applied.  A critical aspect of these preconditioners is the development of approximate Schur complement operators that encode the critical cross-coupling physics of the system.  To demonstrate the flexibility and performance of these methods, the speaker considers the application of these techniques to various forms of resistive MHD models for challenging prototype plasma problems.  These include computational results relevant to aspects of magnetic confinement fusion applications.  Results are presented on robustness, efficiency, and the parallel and algorithmic scaling of the solution methods. 

Speaker’s Bio:

Dr. John N. Shadid is a distinguished member of the technical staff in the Computational Mathematics Department at Sandia National Laboratories and holds an appointment as a national lab professor in the Mathematics Department at the University of New Mexico.  John received a Bachelor of Science and a Master of Science degree in Mechanical Engineering, as well as a Master of Science degree in Mathematics from the University of Wisconsin-Milwaukee.  He earned his Ph.D. in Mechanical Engineering from the University of Minnesota in 1989.  Dr. Shadid has contributed to the fields of applied mathematics, numerical methods, computational algorithms, and software development for solution methods of highly nonlinear coupled multiple-time-scale partial differential equation systems.  He was the co-principal investigator for the Aztec software library, which received a 1997 Research and Development 100 Award and was one of the very first scalable parallel iterative solver libraries.  He has also been the lead principal investigator for several projects developing robust, scalable, implicit finite element reacting flow, MHD, and multifluid electromagnetic plasma system simulation capabilities in support of the U.S. Department of Energy's Office of Science-oriented scientific applications.  In 2018, he was elected as a Society for Industrial and Applied Mathematics Fellow and in 2019 he received the United States Association of Computational Mechanics Thomas J.R. Hughes Medal for Computational Fluid Mechanics.