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SUMMARY:Deterministic Multilevel Methods for Forward and Inverse UQ in PDE
 s - Christoph Schwab (ETH Zürich)
DTSTART:20180409T123000Z
DTEND:20180409T133000Z
UID:TALK103534@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We present the numerical analysis of Quasi Monte-Carlo methods
  for high-dimensional integration applied to forward and inverse uncertain
 ty quantification for elliptic and parabolic PDEs.  Emphasis will be place
 d on the role of parametric holomorphy of data-to-solution maps.  We prese
 nt corresponding results on deterministic quadratures in Bayesian Inversio
 n of parametric PDEs\,  and the related bound on posterior sparsity and (d
 imension-independent)  QMC convergence rates.  Particular attention will b
 e placed on Higher-Order QMC\, and on the interplay between the  structure
  of the representation system of the distributed uncertain input data  (KL
 \, splines\, wavelets\,...) and the structure of QMC weights.  We also rev
 iew stable and efficient generation of interlaced polynomial lattice rules
 \, and the numerical  analysis of multilevel QMC Finite Element PDE discre
 tizations with applications to forward and inverse computational uncertain
 ty quantification.  QMC convergence rates will be compared with those affo
 rded by Smolyak quadrature.  Joint work with Robert Gantner and Lukas Herr
 mann and Jakob Zech (SAM\, ETH) and  Josef Dick\, Thong LeGia and Frances 
 Kuo (Sydney).  References:  [1] R. N. Gantner and L. Herrmann and Ch. Schw
 ab Quasi-Monte Carlo integration for affine-parametric\, elliptic PDEs: lo
 cal supports and product weights\, SIAM J. Numer. Analysis\, 56/1 (2018)\,
  pp. 111-135.  [2] J. Dick and R. N. Gantner and Q. T. Le Gia and Ch. Schw
 ab Multilevel higher-order quasi-Monte Carlo Bayesian estimation\, Math. M
 od. Meth. Appl. Sci.\, 27/5 (2017)\, pp. 953-995.  [3] R. N. Gantner and M
 . D. Peters Higher Order Quasi-Monte Carlo for Bayesian Shape Inversion\, 
 accepted (2018) SINUM\, SAM Report 2016-42.  [4] J. Dick and Q. T. Le Gia 
 and Ch. Schwab Higher order Quasi Monte Carlo integration for holomorphic\
 , parametric operator equations\, SIAM Journ. Uncertainty Quantification\,
  4/1 (2016)\, pp. 48-79  [5] J. Dick and F.Y. Kuo and Q.T. LeGia and Ch. S
 chwab Multi-level higher order QMC Galerkin discretization for affine para
 metric operator equations\, SIAM J. Numer. Anal.\, 54/4 (2016)\, pp. 2541-
 2568 
LOCATION:Seminar Room 1\, Newton Institute
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