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SUMMARY:Tensor methods for higher-dimensional Fokker-Planck equation - Tom
 as Vejchodsky (Academy of Sciences of the Czech Republic)
DTSTART:20160406T104500Z
DTEND:20160406T113000Z
UID:TALK65330@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In order to analyse stochastic chemical systems\, we solve the
  corresponding Fokker-Planck equation numerically. The dimension of this p
 roblem corresponds to the number of chemical species and the standard nume
 rical methods fail for systems with already four or more chemical species 
 due to the so called curse of dimensionality. Using tensor methods we succ
 eeded to solve realistic problems in up to seven dimensions and an academi
 c example of a reaction chain of 20 chemical species. <br><br>In the talk 
 we will present the Fokker-Planck equation and discuss its well-posedness.
  We will describe its discretization based on the finite difference method
  and we will explain the curse of dimensionality. Then we provide the main
  idea of tensor methods. We will identify several types of errors of the p
 resented numerical scheme\, namely the modelling error\, the domain trunca
 tion error\, discretization error\, tensor truncation error\, and the alge
 braic error. We will present an idea that equilibration of these errors ba
 sed on a posteriori error estimates yields considerable savings of the com
 putational time.<br>
LOCATION:Seminar Room 1\, Newton Institute
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