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SUMMARY:Weighted reduced order methods for parametrized PDEs with random i
 nputs - Gianluigi Rozza (SISSA)
DTSTART:20180308T090000Z
DTEND:20180308T094500Z
UID:TALK102229@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In this talk we discuss a weighted approach for the reduction 
 of parametrized partial differential equations with random input\, focusin
 g in particular on weighted approaches based on reduced basis (wRB) [Chen 
 et al.\, SIAM Journal on Numerical Analysis (2013)\; D. Torlo et al.\, sub
 mitted (2017)] and proper orthogonal decomposition (wPOD) [L. Venturi et a
 l.\, submitted (2017)]. We will first present the wPOD approach. A first t
 opic of discussion is related to the choice of samples and respective weig
 hts according to a quadrature formula. Moreover\, to reduce the computatio
 nal effort in the offline stage of wPOD\, we will employ Smolyak quadratur
 e rules. We will then introduce the wRB method for advection diffusion pro
 blems with dominant convection with random input parameters. The issue of 
 the stabilisation of the resulting reduced order model will be discussed i
 n detail. This work is in collaboration with Francesco Ballarin (SISSA\, T
 rieste)\, Davide Torlo (University of Zurich)\, and Luca Venturi (Courant 
 Institute for Mathematical Sciences\, NYC)
LOCATION:Seminar Room 1\, Newton Institute
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