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Applied Math Seminar: Scalable Solution Methods for Multiple-time-scale Plasma Physics Models that Enable Beyond Forward Simulations*

Event Type: 
Seminar
Speaker: 
John Shadid
Event Date: 
Monday, October 31, 2016 - 3:30pm
Location: 
SMLC 356
Audience: 
Faculty/StaffStudentsAlumni/Friends
Sponsor/s: 
Deborah Sulsky

Event Description: 

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. 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. To provide robust and efficient forward solutions and enable efficient beyond forward simulation capabilities effective nonlinear / linear iterative solution methods are required to implement direct-to-steady-state and/or some form of implicit time integration for these multiphysics systems.
 
In this presentation I will discuss issues related to the stable, accurate and efficient time integration, nonlinear, and linear solution of
continuum plasma systems. The discussion will begin with a brief overview of a representative set of magnetohydrodynamics (MHD) and multifluid plasma models. I will then motivate our interest in
implicit methods with a few illustrative examples that compare operator split and semi-implicit approaches, to implicit methods for prototype convection/diffusion/reaction systems.
In the context of implicit solution of plasma systems I will then overview a number of the fully-coupled Newton-Krylov methods that our group employees in solution of large-scale sparse linear / nonlinear systems with a focus on scalable multilevel preconditioning methods.   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.
The discussion of these approaches considers the flexibility, robustness, efficiency, and the parallel and algorithmic scaling of the preconditioning methods.
These results include weak-scaling studies on up to 256K 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 Laboratories. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation,
a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
 
 
Information pertaining to the short discussion on opportunities for students and post docs:
 
 
 
 
 
Coffee and tea will be served in the lounge at 15.00