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CATEGORIES:Applied and Computational Analysis
SUMMARY:Adaptive Intrusive Methods for Forward UQ in PDEs
- Catherine Powell (University of Manchester)
DTSTART;TZID=Europe/London:20240215T150000
DTEND;TZID=Europe/London:20240215T160000
UID:TALK210127AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/210127
DESCRIPTION:In this talk we discuss a so-called intrusive appr
oach for the forward propagation of uncertainty in
PDEs with uncertain coefficients. Specifically\,
we focus on stochastic Galerkin finite element met
hods (SGFEMs). Multilevel variants of such methods
provide polynomial-based surrogates with spatial
coefficients that reside in potentially different
finite element spaces. For elliptic PDEs with diff
usion coefficients represented as affine functions
of countably infinitely many parameters\, well es
tablished theoretical results state that such meth
ods can achieve rates of convergence independent o
f the number of input parameters\, thereby breakin
g the curse of dimensionality. Moreover\, for nice
enough test problems\, it is even possible to pro
ve convergence rates afforded to the chosen finite
element method for the associated deterministic P
DE. However\, achieving these rates in practice u
sing automated computational algorithms remains hi
ghly challenging\, and non-intrusive multilevel sa
mpling methods are often preferred for their ease
of use. We discuss an adaptive framework that is d
riven by a classical hierarchical a posteriori err
or estimation strategy — modified for the more cha
llenging parametric PDE setting — and present nume
rical results.
LOCATION:Centre for Mathematical Sciences\, MR14
CONTACT:Nicolas Boulle
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