Wednesday, May 12

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

11:40 AM-12:25 PM
Room: Capitol North/Center South
Chair: C. T. Kelley, North Carolina State University

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.

David E. Keyes
Old Dominion University & ICASE, NASA Langley Research Center

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MMD, 12/21/98