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UID:news246@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20180716T211540
DTSTART;TZID=Europe/Zurich:20151204T110000
SUMMARY:Seminar in Numerical Analysis: Sebastian Ullmann (TU Darmstadt)
DESCRIPTION:Surrogate models can be used to decrease  the computational cos
 t for uncertainty quantification in the context of  parabolic PDEs with st
 ochastic data. Projection based reduced-order  modeling provides surrogate
 s which inherit the spatial structure of the  solution as well as the unde
 rlying physics. In my talk I focus on the  type of models that is derived 
 by a Galerkin projection onto a proper  orthogonal decomposition (POD) of 
 snapshots of the solution.\\r\\nStandard  techniques assume that all snaps
 hots use one and the same spatial mesh.  I present a generalization for un
 steady adaptive finite elements\, where  the mesh can change from time ste
 p to time step and\, in the case of  stochastic sampling\, from realizatio
 n to realization. I will answer the  following questions: How can the codi
 ng effort for creating such a  reduced-order model be minimized? How can t
 he union of all snapshot  meshes be avoided? What is the main difference b
 etween static and  adaptive snapshots in the error analysis of Galerkin re
 duced-order  models?\\r\\nAs a numerical test case I consider a two-dimens
 ional  viscous Burgers equation with smooth initial data multiplied by a  
 normally distributed random variable. The results illustrate the  converge
 nce properties with respect to the number of POD basis functions  and indi
 cate possible savings of computation time.
X-ALT-DESC:Surrogate models can be used to decrease  the computational cost
  for uncertainty quantification in the context of  parabolic PDEs with sto
 chastic data. Projection based reduced-order  modeling provides surrogates
  which inherit the spatial structure of the  solution as well as the under
 lying physics. In my talk I focus on the  type of models that is derived b
 y a Galerkin projection onto a proper  orthogonal decomposition (POD) of s
 napshots of the solution.\nStandard  techniques assume that all snapshots 
 use one and the same spatial mesh.  I present a generalization for unstead
 y adaptive finite elements\, where  the mesh can change from time step to 
 time step and\, in the case of  stochastic sampling\, from realization to 
 realization. I will answer the  following questions: How can the coding ef
 fort for creating such a  reduced-order model be minimized? How can the un
 ion of all snapshot  meshes be avoided? What is the main difference betwee
 n static and  adaptive snapshots in the error analysis of Galerkin reduced
 -order  models?\nAs a numerical test case I consider a two-dimensional  vi
 scous Burgers equation with smooth initial data multiplied by a  normally 
 distributed random variable. The results illustrate the  convergence prope
 rties with respect to the number of POD basis functions  and indicate poss
 ible savings of computation time. 
DTEND;TZID=Europe/Zurich:20151204T120000
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