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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Quasi-Monte Carlo integration in uncertainty quant
ification of elliptic PDEs with log-Gaussian coeff
icients - Lukas Herrmann (ETH Zürich)
DTSTART;TZID=Europe/London:20190618T154000
DTEND;TZID=Europe/London:20190618T163000
UID:TALK126157AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/126157
DESCRIPTION:Quasi-Monte Carlo (QMC) rules are suitable to over
come the curse of dimension in the numerical integ
ration of high-dimensional integrands.
Also the
convergence rate of essentially first order is su
perior to Monte Carlo sampling.
We study a cla
ss of integrands that arise as solutions of ellipt
ic PDEs with log-Gaussian coefficients.
In part
icular\, we focus on the overall computational cos
t of the algorithm.
We prove that certain mult
ilevel QMC rules have a consistent accuracy and co
mputational cost that is essentially of optimal or
der in terms of the degrees of freedom of the spat
ial Finite Element
discretization for a range
of infinite-dimensional priors.
This is joint w
ork with Christoph Schwab.
References:
[L. Herrmann\, Ch. Schwab: QMC integration for log
normal-parametric\, elliptic PDEs: local supports
and product weights\, Numer. Math. 141(1) pp. 63--
102\, 2019]\,
[L. Herrmann\, Ch. Schwab: Multi
level quasi-Monte Carlo integration with product w
eights for elliptic PDEs with lognormal coefficien
ts\, to appear in ESAIM:M2AN]\,
[L. Herrmann:
Strong convergence analysis of iterative solvers f
or random operator equations\, SAM report\, 2017-3
5\, in review]
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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