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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Tensor methods for higher-dimensional Fokker-Planc
k equation - Tomas Vejchodsky (Academy of Sciences
of the Czech Republic)
DTSTART;TZID=Europe/London:20160406T114500
DTEND;TZID=Europe/London:20160406T123000
UID:TALK65330AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/65330
DESCRIPTION:In order to analyse stochastic chemical systems\,
we solve the corresponding Fokker-Planck equation
numerically. The dimension of this problem corresp
onds to the number of chemical species and the sta
ndard numerical methods fail for systems with alre
ady four or more chemical species due to the so ca
lled curse of dimensionality. Using tensor methods
we succeeded to solve realistic problems in up to
seven dimensions and an academic example of a rea
ction chain of 20 chemical species.

In the
talk we will present the Fokker-Planck equation a
nd discuss its well-posedness. We will describe it
s discretization based on the finite difference me
thod and we will explain the curse of dimensionali
ty. Then we provide the main idea of tensor method
s. We will identify several types of errors of the
presented numerical scheme\, namely the modelling
error\, the domain truncation error\, discretizat
ion error\, tensor truncation error\, and the alge
braic error. We will present an idea that equilibr
ation of these errors based on a posteriori error
estimates yields considerable savings of the compu
tational time.

LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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