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BEGIN:VEVENT
UID:news268@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20180716T221403
DTSTART;TZID=Europe/Zurich:20140307T110000
SUMMARY:Seminar in Numerical Analysis: Fabio Nobile (EPF Lausanne)
DESCRIPTION:We consider the Darcy equation to describe the flow in a satura
 ted porous medium. The permeability of the medium is described as a log-no
 rmal random field\, eventually conditioned to available direct measurement
 s\, to account for its relatively large uncertainty and heterogeneity.\\r\
 \nWe consider perturbation methods based on Taylor expansion of the soluti
 on of the PDE around the nominal permeability value. Successive higher ord
 er corrections to the statistical moments such as pointwise mean and covar
 iance of the solution can be obtained recursively from the computation of 
 high order correlation functions which\, on their turn\, solve high dimens
 ional problems. To overcome the curse of dimensionality in computing and s
 toring such high order correlations\, we adopt a low-rank format\, namely 
 the so called tensor-train (TT) format.\\r\\nWe show that\, on the one han
 d\, the Taylor series does not converge globally\, so that it only makes s
 ense to compute corrections up to a maximum critical order\, beyon which t
 he accuracy of the solution deteriorates insetad of improving. On the othe
 r hand\, we show on some numerical test cases\, the effectiveness of the p
 roposed approach in case of a moderately small variance of the log-normal 
 permeability field.
X-ALT-DESC:We consider the Darcy equation to describe the flow in a saturat
 ed porous medium. The permeability of the medium is described as a log-nor
 mal random field\, eventually conditioned to available direct measurements
 \, to account for its relatively large uncertainty and heterogeneity.\nWe 
 consider perturbation methods based on Taylor expansion of the solution of
  the PDE around the nominal permeability value. Successive higher order co
 rrections to the statistical moments such as pointwise mean and covariance
  of the solution can be obtained recursively from the computation of high 
 order correlation functions which\, on their turn\, solve high dimensional
  problems. To overcome the curse of dimensionality in computing and storin
 g such high order correlations\, we adopt a low-rank format\, namely the s
 o called tensor-train (TT) format.\nWe show that\, on the one hand\, the T
 aylor series does not converge globally\, so that it only makes sense to c
 ompute corrections up to a maximum critical order\, beyon which the accura
 cy of the solution deteriorates insetad of improving. On the other hand\, 
 we show on some numerical test cases\, the effectiveness of the proposed a
 pproach in case of a moderately small variance of the log-normal permeabil
 ity field. 
DTEND;TZID=Europe/Zurich:20140307T120000
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