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UID:news253@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20180716T213628
DTSTART;TZID=Europe/Zurich:20150508T110000
SUMMARY:Seminar in Numerical Analysis: Christian Stohrer (ENSTA ParisTech)
DESCRIPTION:Electromagnetic phenomena can be modeled using Maxwell's equati
 ons.  In particular we are interested in harmonic electromagnetic waves  p
 ropagating through a highly oscillatory material such as e.g. fiber  reinf
 orced plastic. The permittivity and the permeability of such  materials va
 ry on a microscopic length scale. The use of standard edge  finite element
 s is of limited profit\, since the microscopic structure  requires very re
 fined meshes to provide satisfying approximations. This  may easily result
  in computational costs difficult to manage. However\,  if one is only int
 erested in the effective behavior of the solution and  not in the microsco
 pic details\, homogenization techniques can be used to  overcome these dif
 ficulties. In this talk we review first the results  of analytical homogen
 ization results for Maxwell's equations. The goal  of this theory is to re
 place the oscillatory material with an effective  one\, such that the over
 all behavior of the solution remains unchanged.  The solution of the arisi
 ng equations can be solved with standard  numerical methods because the ef
 fective material depends no longer on  the micro scale. In the second part
  of the talk we propose a multiscale  scheme following the framework of th
 e finite element heterogeneous  multiscale method (FE-HMM). Contrary to th
 e discretization of the  analytically homogenized equation\, no effective 
 coefficient must be  precomputed beforehand. We prove that the FE-HMM solu
 tion converges to  the homogenized one for periodic materials and show som
 e numerical  experiments.\\r\\nThis is a joint work with Sonia Fliss and P
 atrick Ciarlet.
X-ALT-DESC:Electromagnetic phenomena can be modeled using Maxwell's equatio
 ns.  In particular we are interested in harmonic electromagnetic waves  pr
 opagating through a highly oscillatory material such as e.g. fiber  reinfo
 rced plastic. The permittivity and the permeability of such  materials var
 y on a microscopic length scale. The use of standard edge  finite elements
  is of limited profit\, since the microscopic structure  requires very ref
 ined meshes to provide satisfying approximations. This  may easily result 
 in computational costs difficult to manage. However\,  if one is only inte
 rested in the effective behavior of the solution and  not in the microscop
 ic details\, homogenization techniques can be used to  overcome these diff
 iculties. In this talk we review first the results  of analytical homogeni
 zation results for Maxwell's equations. The goal  of this theory is to rep
 lace the oscillatory material with an effective  one\, such that the overa
 ll behavior of the solution remains unchanged.  The solution of the arisin
 g equations can be solved with standard  numerical methods because the eff
 ective material depends no longer on  the micro scale. In the second part 
 of the talk we propose a multiscale  scheme following the framework of the
  finite element heterogeneous  multiscale method (FE-HMM). Contrary to the
  discretization of the  analytically homogenized equation\, no effective c
 oefficient must be  precomputed beforehand. We prove that the FE-HMM solut
 ion converges to  the homogenized one for periodic materials and show some
  numerical  experiments.\nThis is a joint work with Sonia Fliss and Patric
 k Ciarlet. 
DTEND;TZID=Europe/Zurich:20150508T120000
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