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BEGIN:VEVENT
DTSTAMP:20200220T091525Z
DTSTART:20200320T140000Z
DTEND:20200320T150000Z
SUMMARY:Alexander Gilbert - Quasi-Monte Carlo methods for the uncertainty
quantification of eigenvalue problems
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}m83-k5cim1n
b-efs5e2
DESCRIPTION:Dr. Alexander Gilbert from Institute for Applied Mathematics
at Heidelberg University will be speaking at this seminar.\nAbstract: E
igenvalue problems are useful for modelling many important physical phen
omena\, ranging from photonic crystal structures to quantum mechanics to
the neutron diffusion criticality problem. In many of these application
s the model parameters are unknown\, in which case one aims to quantify
the uncertainty in the eigenproblem model. With this as motivation\, we
will study an elliptic eigenvalue problem with coefficients that depend
on infinitely many stochastic parameters. The stochasticity in the coeff
icients causes the eigenvalues and eigenfunctions\nto also be stochastic
\, and so our goal will be to compute the expectation of the minimal eig
envalue. In practice\, to approximate this expectation one must: 1) trun
cate the stochastic dimension\; 2) discretise the eigenvalue problem in
space (e.g.\, by finite elements)\; and 3) apply a quadrature rule to es
timate the expected value.In this talk\, we will present a multilevel qu
asi-Monte Carlo method for approximating the expectation of the minimal
eigenvalue\, which is based on a hierarchy of finite element meshes and
truncation dimensions. To improve the sampling efficiency over Monte Car
lo we will use a quasi-Monte Carlo rule to generate the sampling points.
Quasi-Monte Carlo rules are deterministic (or quasi-random) quadrature
rules that are well-suited to high-dimensional integration and can conve
rge at a rate of 1/N\, which is faster than the rate for Monte Carlo. Al
so\, to make each eigenproblem solve on a given level more efficient\, w
e utilise the two-grid scheme from [Xu & Zhou 1999] to obtain the eigenv
alue on the fine mesh from the coarse eigenvalue (and eigenfunction) wit
h a single linear solve.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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