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SUMMARY:Nonlinear Safeguarding for Complex Physics\; Search-less Line-sear
ch
DTSTART;VALUE=DATE-TIME:20180515T165300Z
DTEND;VALUE=DATE-TIME:20180515T170800Z
DTSTAMP;VALUE=DATE-TIME:20200803T231132Z
UID:indico-contribution-396@events.interpore.org
DESCRIPTION:Speakers: Rami Younis (University of Tulsa)\nThis work develop
s the theoretical basis and practical application of a promising class of
safeguarding strategy in the context of the solution of implicit timesteps
for multiphase multicomponent flows in general. \n\nWhile classic globali
zation methods such as the linesearch for sufficient descent are problem i
ndependent\, they require numerous computationally costly evaluations of t
he residual system. Furthermore\, they may overly conservative and result
in small Newton updates. Developments over the past decade have cemented t
he efficacy of component-wise relaxation safeguards as an alternative to g
lobal search methods\, particularly when the relaxation parameter can be d
educed from heuristic arguments at constant cost. These methods however ar
e problem specific in the sense that they require prior information about
the nonlinearity of the numerical flux over the component space at hand. R
ecently\, the ideas of these component-wise numerical flux analyses were g
eneralized to systems of equations where in essence\, a search procedure i
s used to determine a relaxation length. The result is a return to the nee
d for an expensive search procedure involving numerous residual evaluation
s. In this work\, the criterion for an admissible step along a Newton dire
ction is abstracted\; it may be a residual descent criterion\, or a local
Lipschitz estimate. We apply a discretization error analysis and local fun
ctional estimates to then compute the steplength that will satisfy this cr
iterion.\n\nThe damping algorithm is based on viewing the Newton iteration
as a forward Euler discretization of the Newton flow equations. Three a p
osteriori local discretization error estimates are derived\; the first is
an extension of the Poschka method to computably estimate the norm of the
derivative of the Newton step with respect to step-length. This relatively
costly estimate provides an accurate measure of the departure from the Ne
wton flow path. The second estimate is based on Richardson extrapolation\,
and the third involves an extended Adams-Bashford method. We propose to c
ontrol the Newton step length by limiting the estimated local discretizati
on error. The control strategy is conservative far from the solution\, and
can be shown to result in the standard Newton method otherwise. \nComputa
tional results are presented for a series of simulation problems with incr
easing complexity. First\, results for two phase flow simulations demonstr
ate that the proposed method is competitive with\, but not superior to rec
ently proposed trust-region based strategies. For thermal and multicompone
nt problems the method is compared to classic trust-region and line-search
methods. Superior robustness and computational efficiencies are observed\
, and the iteration converges for significantly larger time-step sizes.\n\
nhttps://events.interpore.org/event/2/contributions/396/
LOCATION:New Orleans
URL:https://events.interpore.org/event/2/contributions/396/
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