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CATEGORIES:ps583's list
SUMMARY:Reduced Order Models for Parameterized Hyperbolic
Conservation Laws with Shock Reconstruction - Paul
Constantine\, Stanford University
DTSTART;TZID=Europe/London:20120927T130000
DTEND;TZID=Europe/London:20120927T140000
UID:TALK40198AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/40198
DESCRIPTION:Continued advances in high performance computing a
re enabling\nresearchers in computational science
to simulate more complex physical\nmodels. Such si
mulations can occupy massive supercomputers for\ne
xtended periods of time. Unfortunately\, the cost
of these complex\nsimulations renders parameter st
udies (e.g.\, design optimization or\nuncertainty
quantication) infeasible\, where multiple simulat
ions must\nbe run to explore the space of design p
arameters or uncertain inputs.\nA common fix is to
construct a cheaper reduced order model -- traine
d\non the outputs of a few carefully selected simu
lation runs -- for use\nin the parameter study.\n\
nModel reduction for large-scale simulations is an
active research\nfield. Techniques such as reduce
d basis methods and various\ninterpolation schemes
have been used successfully to approximate the\ns
imulation output at new parameter values at a frac
tion of the\ncomputational cost of a full simulati
on. These methods perform best\nwhen the solution
is smooth with respect to the model parameters. Th
e\nsolution of nonlinear conservation laws are kno
wn to develop\ndiscontinuities in space even for s
mooth initial data. These spatial\ndiscontinuities
typically imply discontinuities in the parameter\
nspace\, which severely diminish the performance o
f standard model\nreduction methods.\n\nWe present
a method for constructing an accurate reduced ord
er model\nof the solution to a parameterized\, non
linear conservation law. We use\na standard method
for an initial guess and propose a metric for\nde
termining regions in space/time where the standard
method yields a\npoor approximation. We then retu
rn to the conservation law and correct\nthe region
s of low accuracy. We will describe the method in
general\nand present results on the inviscid Euler
equations with parameterized\ninitial conditions.
\n
LOCATION:Lecture Theatres - LT1\, Cambridge University Depa
rtment of Engineering\, Inglis Building
CONTACT:Pranay Seshadri
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