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

Loïc Giraldi, Alexander Litvinenko, Dishi Liu, Hermann G. Matthies, Anthony Nouy

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

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).
Original languageEnglish (US)
Pages (from-to)A2720-A2744
Number of pages1
JournalSIAM Journal on Scientific Computing
Volume36
Issue number6
DOIs
StatePublished - Jan 2014

Fingerprint Dive into the research topics of 'To Be or Not to Be Intrusive? The Solution of Parametric and Stochastic Equations---the “Plain Vanilla” Galerkin Case'. Together they form a unique fingerprint.

Cite this