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SUMMARY:UQ: does it require efficient linear algebra? - David Silvester (U
 niversity of Manchester)
DTSTART:20180619T130000Z
DTEND:20180619T140000Z
UID:TALK107305@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We discuss the key role that bespoke linear algebra plays in m
 odelling PDEs with random coefficients using stochastic Galerkin approxima
 tion methods.  As a specific example\,  we consider nearly incompressible 
 linear elasticity problems with an uncertain spatially varying Young&#39\;
 s modulus. The uncertainty is modelled with a finite set of parameters wit
 h prescribed probability distribution.  We introduce a novel three-field m
 ixed variational formulation of the PDE model and focus on the efficient s
 olution of the associated high-dimensional indefinite linear system of equ
 ations. Eigenvalue bounds for the preconditioned system are established an
 d shown to be independent of the discretisation parameters and the Poisson
  ratio. If time permits\, we will also discuss the efficient solution of i
 ncompressible fluid flow problems with uncertain viscosity.  This is joint
  work with Arbaz Khan and Catherine Powell.
LOCATION:Seminar Room 2\, Newton Institute
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