To be or not to be intrusive? The solution of parametric and stochastic equations - the "plain vanilla" Galerkin case

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, To be or not to be intrusive? The solution of parametric and stochastic equations - the "plain vanilla" Galerkin case. SIAM Journal on Scientific Computing (Vol. 36, Issue 6).
Loïc Giraldi, Alexander Litvinenko, Dishi Liu, Hermann G. Matthies, Anthony Nouy
Uncertainty quantification, stochastic Galerkin approximation, parametric problems, stochastic equation, coupled system, non-intrusive computation
2014

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 of 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 the equation for a given parameter value - this may be a software component or a program - it is evident that this can independently solve for the parameter values to be interpolated. Such uncoupled methods which allow the use of the original solver are classed as "non-intrusive". By extension, all other methods which produce some kind of coupled system are often - in our view prematurely - classed as "intrusive". We show for simple Galerkin formulations of the parametric problem - which generally produce coupled systems - how one may compute the approximation in a non-intusive way.

DOI: 10.1137/130942802