Seminar Announcement

Krylov, Lagrange, Newton, and Schwarz: Combinations and Permutations

David Keyes
Mathematics & Statistics Dept., Old Dominion University
Institute for Scientific Computing Research, LLNL
Institute for Computer Applications in Science and Engineering, NASA Langely

Wednesday, October 6, 1999
2:00 - 3:00 p.m.
Bldg. 921, Room 137

Newton-Krylov-Schwarz (NKS) is among the leading rootfinding techniques for large-scale nonlinear systems arising from the implicit discretization of partial differential equations on parallel computers. Globalized versions of the matrix-free inexact Newton-Krylov technique provide nonlinear robustness with parsimonious Jacobian access. Additive Schwarz preconditionings (including multilevel forms) provide linear robustness with good concurrency and locality properties. In this presentation, the speaker will illustrate NKS technique in fluid mechanics and radiation transport problems and will explore two extensions. First, he will discuss how to cast Lagrangian-based PDE-constrained optimization problems in the NKS framework, in an attempt to leverage parallel analysis codes for design purposes. Second, in a retreat from the "brute force'' framework of a global Newton method, motivated by increasing complexity in both applications and computer architecture, he will discuss a Schwarz-Newton-Krylov method in which adaptively selected, loosely coupled subdomain problems are solved in a nonlinear Schwarz outer iteration.

This seminar is hosted by the Computational Sciences and Mathematics Research Department at Sandia National Labs in Livermore, CA. For more information on this or other events, visit http://csmr.ca.sandia.gov/news.html. Visitors from outside Sandia require advance arrangements in order to attend. For more information, please contact the CSMR office management assistant Doretha Smith at dahall@sandia.gov or (925) 294-4630.