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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:TALK126157@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 sol
 utions of elliptic PDEs with log-Gaussian coefficients.<br>In particular\,
  we focus on the overall computational cost of the algorithm. <br>We prove
  that certain multilevel QMC rules have a consistent accuracy and computat
 ional cost that is essentially of optimal order in terms of the degrees of
  freedom of the spatial Finite Element <br>discretization for a range of i
 nfinite-dimensional priors.<br>This is joint work with Christoph Schwab.<b
 r><br>References: <br>[L. Herrmann\, Ch. Schwab: QMC integration for logno
 rmal-parametric\, elliptic PDEs: local supports and product weights\, Nume
 r. Math. 141(1) pp. 63--102\, 2019]\, <br>[L. Herrmann\, Ch. Schwab: Multi
 level quasi-Monte Carlo integration with product weights for elliptic PDEs
  with lognormal coefficients\, to appear in ESAIM:M2AN]\, <br>[L. Herrmann
 : Strong convergence analysis of iterative solvers for random operator equ
 ations\, SAM report\, 2017-35\, in review]
LOCATION:Seminar Room 1\, Newton Institute
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