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BEGIN:VEVENT
UID:news248@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20180716T212124
DTSTART;TZID=Europe/Zurich:20151009T110000
SUMMARY:Seminar in Numerical Analysis: Andrea Barth (University of Stuttgar
 t)
DESCRIPTION:Multilevel Monte Carlo methods  were introduced to lower the co
 mputational complexity for the  calculation of\, for instance\, the expect
 ation of a random quantity. More  precisely\, in comparison to standard Mo
 nte Carlo methods the  computational complexity is (asymptotically) equal 
 to the calculation of  one sample of the problem on the finest grid used. 
 The price to pay for  this increase in efficiency is that the problem need
 s to be solved not  only on one (fine) grid\, but on a hierarchy of discre
 tizations. This  implies first that the solution has to be represented on 
 all grids and  second\, that the variance of the detail (the difference of
  approximate  solutions on two consecutive grids) converges with the refin
 ement of the  grid.\\r\\nIn this talk\, I will give an introduction to mul
 tilevel  Monte Carlo methods in the case when the variance of the detail d
 oes not  converge uniformly. The idea is illustrated by the calculation of
  the  expectation for an elliptic problem with a random multiscale coeffic
 ient  and then extended to approximations of statistical solutions to the 
  Navier-Stokes equations.
X-ALT-DESC:Multilevel Monte Carlo methods  were introduced to lower the com
 putational complexity for the  calculation of\, for instance\, the expecta
 tion of a random quantity. More  precisely\, in comparison to standard Mon
 te Carlo methods the  computational complexity is (asymptotically) equal t
 o the calculation of  one sample of the problem on the finest grid used. T
 he price to pay for  this increase in efficiency is that the problem needs
  to be solved not  only on one (fine) grid\, but on a hierarchy of discret
 izations. This  implies first that the solution has to be represented on a
 ll grids and  second\, that the variance of the detail (the difference of 
 approximate  solutions on two consecutive grids) converges with the refine
 ment of the  grid.\nIn this talk\, I will give an introduction to multilev
 el  Monte Carlo methods in the case when the variance of the detail does n
 ot  converge uniformly. The idea is illustrated by the calculation of the 
  expectation for an elliptic problem with a random multiscale coefficient 
  and then extended to approximations of statistical solutions to the  Navi
 er-Stokes equations. 
DTEND;TZID=Europe/Zurich:20151009T120000
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