Model reduction based on proper generalized decomposition for the stochastic steady incompressible navier-stokes equations

L. Tamellini; O. Le Maître; A. Nouy

doi:10.1137/120878999

Model reduction based on proper generalized decomposition for the stochastic steady incompressible navier-stokes equations

L. Tamellini, O. Le Maître, A. Nouy

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

32 Scopus citations

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).

Original language	English (US)
Pages (from-to)	A1089-A1117
Journal	SIAM Journal on Scientific Computing
Volume	36
Issue number	3
DOIs	https://doi.org/10.1137/120878999
State	Published - 2014

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This author’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’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’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.

Keywords

Galerkin method
Model reduction
Reduced basis
Stochastic navier-stokes equations
Uncertainty quantification

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1137/120878999

Cite this

@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).",

keywords = "Galerkin method, Model reduction, Reduced basis, Stochastic navier-stokes equations, Uncertainty quantification",

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",

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 Publications",

number = "3",

}

TY - JOUR

T1 - Model reduction based on proper generalized decomposition for the stochastic steady incompressible navier-stokes equations

AU - Tamellini, L.

AU - Le Maître, O.

AU - Nouy, A.

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: This author’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’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’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.

PY - 2014

Y1 - 2014

N2 - 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).

AB - 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).

KW - Galerkin method

KW - Model reduction

KW - Reduced basis

KW - Stochastic navier-stokes equations

KW - Uncertainty quantification

UR - http://www.scopus.com/inward/record.url?scp=84903596030&partnerID=8YFLogxK

U2 - 10.1137/120878999

DO - 10.1137/120878999

M3 - Article

AN - SCOPUS:84903596030

SN - 1064-8275

VL - 36

SP - A1089-A1117

JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

IS - 3

ER -

Model reduction based on proper generalized decomposition for the stochastic steady incompressible navier-stokes equations

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this