BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Nonlinear Preconditioning for Implicit Solution of Discretized PDE
 s - David Keyes\, King Abdullah University of Science and Technology
DTSTART:20240927T130000Z
DTEND:20240927T140000Z
UID:TALK220105@talks.cam.ac.uk
CONTACT:Chris Richardson
DESCRIPTION:Nonlinear preconditioning refers to transforming a nonlinear a
 lgebraic system to a form for which Newton-type algorithms have improved s
 uccess through quicker advance to the domain of quadratic convergence. We 
 place these methods\, which go back at least as far as the Additive Schwar
 z Preconditioned Inexact Newton (ASPIN\, 2002)\, in the context of a proli
 feration of variations distinguished by being left- or right-sided\, multi
 plicative or additive\, non-overlapping or overlapping\, and partitioned b
 y field\, subdomain\, or other criteria\, as described in a recent special
  issue of J Comp Phys dedicated to Roland Glowinski [Liu et al.\, 2024]. W
 e present the Nonlinear Elimination Preconditioned Inexact Newton (NEPIN\,
  2021)\, which is based on a heuristic bad/good heuristic splitting of equ
 ations and corresponding degrees of freedom. We augment basic forms of non
 linear preconditioning with three features of practical interest: a cascad
 ic identification of the bad discrete equation set\, an adaptive switchove
 r to ordinary Newton as the domain of convergence is approached\, and erro
 r bounds on output functionals of the solution. Various nonlinearly stiff 
 algebraic and model PDE problems are considered for insight and we illustr
 ate performance advantage and scaling potential on challenging two-phase f
 lows in porous media\, as well as some early results in second-order train
 ing methods for neural networks.
LOCATION:Institute for Energy and Environmental Flows\, CB3 0EZ
END:VEVENT
END:VCALENDAR