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BEGIN:VEVENT
UID:news237@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20180716T204932
DTSTART;TZID=Europe/Zurich:20161021T110000
SUMMARY:Seminar in Numerical Analysis: Steffen Börm (Universität Kiel)
DESCRIPTION:In the context of stochastic partial differential equation\, we
  are  frequently faced with equations in high-dimensional domains. In orde
 r to  obtain efficient numerical methods for these equations\, we have to 
 take  local regularity properties of the solution into account\, e.g.\, by
   using locally refined finite element meshes. Extending standard meshing 
  algorithms to higher dimensions poses a significant challenge.\\r\\nWe pr
 opose an alternative: the Galerkin trial space is  constructed using a par
 tition of unity. By multiplying local cut-off  functions with polynomials\
 , we can obtain discretizations of arbitrary  order\, and local grid refin
 ement can be realized by reducing the  supports of the cut-off functions. 
 The main challenge lies in the  construction of the corresponding system m
 atrix\, since even determining  the sparsity pattern involves interactions
  between cut-off functions on  different levels of the mesh hierarchy.\\r\
 \nOur approach leads to a sparse system matrix\, the basis functions  are 
 convenient tensor products of functions on lower-dimensional  domains\, an
 d local regularity can be exploited by variable-order  interpolation in or
 der to obtain close to optimal complexity.
X-ALT-DESC:In the context of stochastic partial differential equation\, we 
 are  frequently faced with equations in high-dimensional domains. In order
  to  obtain efficient numerical methods for these equations\, we have to t
 ake  local regularity properties of the solution into account\, e.g.\, by 
  using locally refined finite element meshes. Extending standard meshing  
 algorithms to higher dimensions poses a significant challenge.\nWe propose
  an alternative: the Galerkin trial space is  constructed using a partitio
 n of unity. By multiplying local cut-off  functions with polynomials\, we 
 can obtain discretizations of arbitrary  order\, and local grid refinement
  can be realized by reducing the  supports of the cut-off functions. The m
 ain challenge lies in the  construction of the corresponding system matrix
 \, since even determining  the sparsity pattern involves interactions betw
 een cut-off functions on  different levels of the mesh hierarchy.\nOur app
 roach leads to a sparse system matrix\, the basis functions  are convenien
 t tensor products of functions on lower-dimensional  domains\, and local r
 egularity can be exploited by variable-order  interpolation in order to ob
 tain close to optimal complexity. 
DTEND;TZID=Europe/Zurich:20161021T120000
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