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SUMMARY:Quasi-Monte Carlo integration in uncertainty quantification of ell
 iptic PDEs with log-Gaussian coefficients - Lukas Herrmann (ETH Zürich)
DTSTART:20190618T144000Z
DTEND:20190618T153000Z
UID:TALK126160@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Quasi-Monte Carlo (QMC) rules are suitable to overcome the cur
 se of dimension in the numerical integration of high-dimensional integrand
 s.<br> Also the convergence rate of essentially first order is superior to
  Monte Carlo sampling. <br> We study a class of integrands that arise as s
 olutions of elliptic PDEs with log-Gaussian coefficients.<br> In particula
 r\, we focus on the overall computational cost of the algorithm. <br> We p
 rove that certain multilevel QMC rules have a consistent accuracy and comp
 utational cost that is essentially of optimal order in terms of the degree
 s of freedom of the spatial Finite Element <br> discretization for a range
  of infinite-dimensional priors.<br> This is joint work with Christoph Sch
 wab.<br> <br> References: <br> [L. Herrmann\, Ch. Schwab: QMC integration 
 for lognormal-parametric\, elliptic PDEs: local supports and product weigh
 ts\, Numer. Math. 141(1) pp. 63--102\, 2019]\, <br> [L. Herrmann\, Ch. Sch
 wab: Multilevel quasi-Monte Carlo integration with product weights for ell
 iptic PDEs with lognormal coefficients\, to appear in ESAIM:M2AN]\, <br> [
 L. Herrmann: Strong convergence analysis of iterative solvers for random o
 perator equations\, SAM report\, 2017-35\, in review]
LOCATION:Seminar Room 1\, Newton Institute
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