Numerical Analysis Seminar

Date: February 21, 2018

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: John N. Shadid, Sandia National Laboratories

Title: On Scalable Solution of Implicit FE Continuum Plasma Physics Models

Abstract: 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. The resulting systems are characterized by strong nonlinear and nonsymmetric coupling of fluid and electromagnetic phenomena, as well as the significant range of time- and length-scales that these interactions produce. 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 and variational multiscale (VMS) methods, and structure-preserving (physics compatible) approaches. For effective long-time-scale integration of these systems the implicit representation of at least a subset of the operators is required. Two well-structured approaches, of recent interest, are fully-implicit and implicit-explicit (IMEX) type time-integration methods employing Newton-Krylov type nonlinear/linear iterative solvers. To enable robust, scalable and efficient solution of the large-scale sparse linear systems generated by a 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. To demonstrate the flexibility of implicit/IMEX FE discretizations and the fully-coupled Newton-Krylov-AMG solution approaches various forms of resistive magnetohydrodynamic (MHD) and multifluid electromagnetic plasma models are considered. In this context, we first briefl