@article{c05bded2081340218f80e51a73bf286f,

title = "Model Reduction Based on Proper Generalized Decomposition for the Stochastic Steady Incompressible Navier--Stokes Equations",

abstract = "In this paper we consider a proper generalized decomposition method to solve the steady incompressible Navier-Stokes equations with random Reynolds number and forcing term. The aim of such a technique is to compute a low-cost reduced basis approximation of the full stochastic Galerkin solution of the problem at hand. A particular algorithm, inspired by the Arnoldi method for solving eigenproblems, is proposed for an efficient greedy construction of a deterministic reduced basis approximation. This algorithm decouples the computation of the deterministic and stochastic components of the solution, thus allowing reuse of preexisting deterministic Navier-Stokes solvers. It has the remarkable property of only requiring the solution of m uncoupled deterministic problems for the construction of an m-dimensional reduced basis rather than M coupled problems of the full stochastic Galerkin approximation space, with m l M (up to one order of magnitudefor the problem at hand in this work). {\textcopyright} 2014 Society for Industrial and Applied Mathematics.",

author = "L. Tamellini and {Le Ma{\^i}tre}, O. and A. Nouy",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: This author{\textquoteright}s work was supported by theItalian grant FIRB-IDEAS (Project RBID08223Z) “Advanced numerical techniques for uncertaintyquantification in engineering and life science problems.” He also received support from the Centerfor ADvanced MOdeling Science (CADMOS).This author{\textquoteright}s work was partially supportedby GNR MoMaS (ANDRA, BRGM, CEA, EdF, IRSN, PACEN-CNRS) and by the French NationalResearch Agency (Grants ANR-08-JCJC-0022 and ANR-2010-BLAN-0904) and in part by the U.S.Department of Energy, Office of Advanced Scientific Computing Research, Award DE-SC0007020,and the SRI Center for Uncertainty Quantification at the King Abdullah University of Science andTechnology.This author{\textquoteright}s work was partially supported by GNR MoMaS (ANDRA, BRGM, CEA,EdF, IRSN, PACEN-CNRS) and by the French National Research Agency (Grants ANR-08-JCJC-0022 and ANR-2010-BLAN-0904). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2014",

month = jan,

doi = "10.1137/120878999",

language = "English (US)",

volume = "36",

pages = "A1089--A1117",

journal = "SIAM Journal on Scientific Computing",

issn = "1064-8275",

publisher = "Society for Industrial and Applied Mathematics",

number = "3",

}