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SUMMARY:SCS: David Keyes (KAUST)
DTSTART:20240910T140000Z
DTEND:20240910T150000Z
DTSTAMP:20241103T231300Z
UID:indico-event-3989@indico.flatironinstitute.org
DESCRIPTION:Nonlinear Preconditioning for Implicit Solution of Discretized
PDEs\nNonlinear preconditioning refers to transforming a nonlinear algebr
aic system to a form for which Newton-type algorithms have improved succes
s through quicker advance to the domain of quadratic convergence. We place
these methods\, which go back at least as far as the Additive Schwarz Pre
conditioned Inexact Newton (ASPIN\, 2002)\, in the context of a proliferat
ion of variations distinguished by being left- or right-sided\, multiplica
tive or additive\, non-overlapping or overlapping\, and partitioned by fie
ld\, subdomain\, or other criteria\, as described in a recent special issu
e of J Comp Phys dedicated to Roland Glowinski [Liu et al.\, 2024]. We pr
esent the Nonlinear Elimination Preconditioned Inexact Newton (NEPIN\, 202
1)\, which is based on a heuristic bad/good heuristic splitting of equatio
ns and corresponding degrees of freedom. We augment basic forms of nonline
ar preconditioning with three features of practical interest: a cascadic i
dentification of the bad discrete equation set\, an adaptive switchover to
ordinary Newton as the domain of convergence is approached\, and error bo
unds on output functionals of the solution. Various nonlinearly stiff alge
braic and model PDE problems are considered for insight and we illustrate
performance advantage and scaling potential on challenging two-phase flows
in porous media\, as well as some early results in second-order training
methods for neural networks.\n\nhttps://indico.flatironinstitute.org/event
/3989/
LOCATION:3rd floor classroom (162)
URL:https://indico.flatironinstitute.org/event/3989/
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