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SUMMARY:Reduced Order Models for Parameterized Hyperbolic Conservation Law
 s with Shock Reconstruction - Paul Constantine\, Stanford University
DTSTART:20120927T120000Z
DTEND:20120927T130000Z
UID:TALK40198@talks.cam.ac.uk
CONTACT:Pranay Seshadri
DESCRIPTION:Continued advances in high performance computing are enabling\
 nresearchers in computational science to simulate more complex physical\nm
 odels. Such simulations can occupy massive supercomputers for\nextended pe
 riods of time. Unfortunately\, the cost of these complex\nsimulations rend
 ers parameter studies (e.g.\, design optimization or\nuncertainty quantic
 ation) infeasible\, where multiple simulations must\nbe run to explore the
  space of design parameters or uncertain inputs.\nA common fix is to const
 ruct a cheaper reduced order model -- trained\non the outputs of a few car
 efully selected simulation runs -- for use\nin the parameter study.\n\nMod
 el reduction for large-scale simulations is an active research\nfield. Tec
 hniques such as reduced basis methods and various\ninterpolation schemes h
 ave been used successfully to approximate the\nsimulation output at new pa
 rameter values at a fraction of the\ncomputational cost of a full simulati
 on. These methods perform best\nwhen the solution is smooth with respect t
 o the model parameters. The\nsolution of nonlinear conservation laws are k
 nown to develop\ndiscontinuities in space even for smooth initial data. Th
 ese spatial\ndiscontinuities typically imply discontinuities in the parame
 ter\nspace\, which severely diminish the performance of standard model\nre
 duction methods.\n\nWe present a method for constructing an accurate reduc
 ed order model\nof the solution to a parameterized\, nonlinear conservatio
 n law. We use\na standard method for an initial guess and propose a metric
  for\ndetermining regions in space/time where the standard method yields a
 \npoor approximation. We then return to the conservation law and correct\n
 the regions of low accuracy. We will describe the method in general\nand p
 resent results on the inviscid Euler equations with parameterized\ninitial
  conditions.\n
LOCATION:Lecture Theatres - LT1\, Cambridge University Department of Engin
 eering\, Inglis Building
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