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SUMMARY:Low-rank cross approximation algorithms for the solution of stocha
 stic PDEs - Sergey Dolgov (University of Bath)
DTSTART:20180307T110000Z
DTEND:20180307T114500Z
UID:TALK102223@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Co-authors: Robert Scheichl		(University of Bath)       
  <br></span><span><br>We consider the approximate solution of parametric P
 DEs using the low-rank Tensor Train (TT) decomposition. Such parametric PD
 Es arise for example in uncertainty quantification problems in engineering
  applications. We propose an algorithm that is a hybrid of the alternating
  least squares and the TT cross methods. It computes a TT approximation of
  the whole solution\, which is particularly beneficial when multiple quant
 ities of interest are sought. The new algorithm exploits and preserves the
  block diagonal structure of the discretized operator in stochastic colloc
 ation schemes. This disentangles computations of the spatial and parametri
 c degrees of freedom in the TT representation. In particular\, it only req
 uires solving independent PDEs at a few parameter values\, thus allowing t
 he use of existing high performance PDE solvers. We benchmark the new algo
 rithm on the stochastic diffusion equation against quasi-Monte Carlo and d
 imension-adaptive sparse grids methods. For sufficiently smooth random fie
 lds the new approach is orders of magnitude faster. </span>
LOCATION:Seminar Room 1\, Newton Institute
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