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DTSTAMP:20190719T085745Z
LOCATION:HG D 3.2
DTSTART;TZID=Europe/Stockholm:20190614T120000
DTEND;TZID=Europe/Stockholm:20190614T123000
UID:submissions.pasc-conference.org_PASC19_sess112_msa227@linklings.com
SUMMARY:Acceleration of Parallel Methods for Stochastic Elliptic Equations
 : A Domain Decomposition Approach
DESCRIPTION:Minisymposium\nComputer Science and Applied Mathematics, Emerg
 ing Application Domains, Engineering\n\nAcceleration of Parallel Methods f
 or Stochastic Elliptic Equations: A Domain Decomposition Approach\n\nReis,
  Congedo, Le Maître\n\nThe resolution of stochastic elliptic equations wit
 h random coefficients, using Monte Carlo methods (MC), can be very costly 
 as they routinely require to solve thousands of samples to obtain converge
 d statistics. The availability of efficient solvers is then crucial. We us
 e domain decomposition methods, because of their parallel features, and we
  develop new strategies to exploit the characteristics and structure of th
 e stochastic problem in the parallel context. In this work, we consider th
 e additive Schwartz Method (SM), where the parallel resolution of <em
 >local</em> elliptic problems is used to update the sub-domains' boundary 
 values. We proposed different preconditioners to improve the convergence r
 ate of the SM and reduce the number of parallel solves. Specifically, we p
 ropose a stochastic preconditioner, that is depending on each sample of th
 e problem. This preconditioner is the ideal preconditioner corresponding t
 o a truncated approximation of random coefficient field, derived from its 
 Karhunen-Loève expansion. Thanks to the resulting finite-dimensiona
 l representation of the coefficient field, a Polynomial Chaos expansion of
  the preconditioner is constructed, in an off-line stage, to make the appr
 oach very cost-effective at the sampling stage. We demonstrate the potenti
 al of the proposed approach and compare it with classical alternatives, su
 ch as the mean-based preconditioning.
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