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To Be or Not to Be Intrusive? The Solution of Parametric and Stochastic Equations---the “Plain Vanilla” Galerkin Case

Loïc, Giraldi and Litvinenko, Alexander and Liu, Dishi and Matthies, Hermann G. and Nouy, Anthony (2014) To Be or Not to Be Intrusive? The Solution of Parametric and Stochastic Equations---the “Plain Vanilla” Galerkin Case. SIAM Journal on Scientific Computing, 36 (6), A2720-A2744. SIAM - Society for Industrial and Applied Mathematics. DOI: 10.1137/130942802 ISSN 0196-5204

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Official URL: http://epubs.siam.org/doi/abs/10.1137/130942802

Abstract

In parametric equations---stochastic equations are a special case---one may want to approximate the solution such that it is easy to evaluate its dependence on the parameters. Interpolation in the parameters is an obvious possibility---in this context often labeled as a collocation method. In the frequent situation where one has a “solver” for a given fixed parameter value, this may be used “nonintrusively” as a black-box component to compute the solution at all the interpolation points independently of each other. By extension, all other methods, and especially simple Galerkin methods, which produce some kind of coupled system, are often classed as “intrusive.” We show how, for such “plain vanilla” Galerkin formulations, one may solve the coupled system in a nonintrusive way, and even the simplest form of block-solver has comparable efficiency. This opens at least two avenues for possible speed-up: first, to benefit from the coupling in the iteration by using more sophisticated block-solvers and, second, the possibility of nonintrusive successive rank-one updates as in the proper generalized decomposition (PGD).

Item URL in elib:https://elib.dlr.de/92922/
Document Type:Article
Title:To Be or Not to Be Intrusive? The Solution of Parametric and Stochastic Equations---the “Plain Vanilla” Galerkin Case
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Loïc, GiraldiUNSPECIFIEDUNSPECIFIED
Litvinenko, AlexanderUNSPECIFIEDUNSPECIFIED
Liu, Dishidishi.liu (at) dlr.deUNSPECIFIED
Matthies, Hermann G.TU BraunschweigUNSPECIFIED
Nouy, AnthonyUNSPECIFIEDUNSPECIFIED
Date:November 2014
Journal or Publication Title:SIAM Journal on Scientific Computing
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Volume:36
DOI :10.1137/130942802
Page Range:A2720-A2744
Publisher:SIAM - Society for Industrial and Applied Mathematics
ISSN:0196-5204
Status:Published
Keywords:stochastic Galerkin, nonintrusive Galerkin, uncertainty quantification
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:fixed-wing aircraft
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - Simulation and Validation
Location: Braunschweig
Institutes and Institutions:Institute of Aerodynamics and Flow Technology > C²A²S²E - Center for Computer Applications in AeroSpace Science and Engineering
Deposited By: Liu, Dishi
Deposited On:03 Dec 2014 14:24
Last Modified:06 Sep 2019 15:29

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