For more information about this meeting, contact Victor Nistor, Jinchao Xu, Stephanie Zerby, Xiantao Li, Yuxi Zheng, Hope Shaffer.

Title: | Scalable Implicit Solution Methods for Multiple-time-scale Multiphysics Systems: Applications from CFD, Transport/Reaction, and MHD* |
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Seminar: | Computational and Applied Mathematics Colloquium |

Speaker: | J.N. Shadid, Sandia Natl. Lab. |

Abstract: | |

A current challenge before the computational science and numerical mathematics community is the efficient computational solution of multiphysics systems. These systems are strongly coupled, highly nonlinear and characterized by multiple physical phenomena that span a very large range of length- and time-scales. These interacting, nonlinear, multiple time-scale physical mechanisms can balance to produce steady-state behavior, nearly balance to evolve a solution on a dynamical time scale that is long relative to the component time-scales, or can be dominated by just a few fast modes. These characteristics make the scalable, robust, accurate, and efficient computational solution of these systems extremely challenging. This presentation will discuss issues related to the stable, accurate and efficient time integration, nonlinear, and linear solution of multiphysics systems. The discussion will begin with an illustrative example that compares operator-split to fully-implicit methods. The talk will then continue with an overview of a number of the important fully-coupled solution methods that our research group has applied to the solution of coupled multiple-time-scale multi-physics systems. These solution methods include, fully-implicit time integration, direct-to-steady-state solution methods, continuation, bifurcation, and optimization techniques that are based on Newton-Krylov iterative solvers. 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. 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 decomposition methods and physics-based preconditioning approaches that reduce the coupled systems into a set of simplified systems to which multilevel methods are applied. The multilevel preconditioners are then compared to standard variable overlap additive one-level Schwarz domain decomposition type preconditioners. To demonstrate the capability of these methods representative results are presented for the solution of transport/reaction and resistive magnetohydrodynamic systems with stabilized finite element methods. In this context robustness, efficiency, and the parallel and algorithmic scaling of solution methods are discussed. These results will include the solution of systems with up to a billion unknows on 100K cores of current large-scale parallel architectures. *This work was partially supported by the DOE office of Science Applied Math Program at Sandia National Laboratory. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DEM-AC04-94AL85000. |

### Room Reservation Information

Room Number: | MB106 |
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Date: | 11 / 02 / 2012 |

Time: | 03:35pm - 04:25pm |