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DTSTART:19810329T020000
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BEGIN:VEVENT
UID:news274@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20180716T231504
DTSTART;TZID=Europe/Zurich:20131011T110000
SUMMARY:Seminar in Numerical Analysis: Maya de Buhan (Université Paris Des
 cartes)
DESCRIPTION:In this talk\, we propose a new method to solve the following i
 nverse  problem: we aim at reconstructing\, from boundary measurements\, t
 he  location\, the shape and the wave propagation speed of an unknown  obs
 tacle surrounded by a medium whose properties are known. Our strategy  com
 bines two methods recently developed by the authors:\\r\\n1 - the  Time-Re
 versed Absorbing Condition method: It combines time reversal  techniques a
 nd absorbing boundary conditions to reconstruct and  regularize the signal
  in a truncated domain that encloses the obstacle.  This enables us to red
 uce the size of the computational domain where we  solve the inverse probl
 em\, now from virtual internal measurements.\\r\\n2  - the Adaptive Invers
 ion method: It is an inversion method which looks  for the value of the un
 known wave propagation speed in a basis composed  by eigenvectors of an el
 liptic operator. Then\, it uses an iterative  process to adapt the mesh an
 d the basis and improve the reconstruction.\\r\\nWe  present several numer
 ical examples in two dimensions to illustrate the  efficiency of the combi
 nation of both methods. In particular\, our  strategy allows (a) to reduce
  the computational cost\, (b) to stabilize  the inverse problem and (c) to
  improve the precision of the results.
X-ALT-DESC:In this talk\, we propose a new method to solve the following in
 verse  problem: we aim at reconstructing\, from boundary measurements\, th
 e  location\, the shape and the wave propagation speed of an unknown  obst
 acle surrounded by a medium whose properties are known. Our strategy  comb
 ines two methods recently developed by the authors:\n1 - the  Time-Reverse
 d Absorbing Condition method: It combines time reversal  techniques and ab
 sorbing boundary conditions to reconstruct and  regularize the signal in a
  truncated domain that encloses the obstacle.  This enables us to reduce t
 he size of the computational domain where we  solve the inverse problem\, 
 now from virtual internal measurements.\n2  - the Adaptive Inversion metho
 d: It is an inversion method which looks  for the value of the unknown wav
 e propagation speed in a basis composed  by eigenvectors of an elliptic op
 erator. Then\, it uses an iterative  process to adapt the mesh and the bas
 is and improve the reconstruction.\nWe  present several numerical examples
  in two dimensions to illustrate the  efficiency of the combination of bot
 h methods. In particular\, our  strategy allows (a) to reduce the computat
 ional cost\, (b) to stabilize  the inverse problem and (c) to improve the 
 precision of the results. 
DTEND;TZID=Europe/Zurich:20131011T120000
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