01890nas a2200145   4500008004100000245011800041210006900159260001300228520137300241653003501614100001801649700002001667700002101687856003601708       2013                        en  d00aA combination between the reduced basis method and the ANOVA expansion: On the computation of sensitivity indices0 acombination between the reduced basis method and the ANOVA expan  bElsevier3 a<p>We consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance of a three-step RB-ANOVA-RB method. This is a combination of the reduced basis (RB) method and the analysis of variations (ANOVA) expansion, aiming at compressing the parameter space without affecting the accuracy of the output. The idea of this method is to compute a first (coarse) RB approximation of the output of interest involving all the parameter components, but with a large tolerance on the a posteriori error estimate; then, we evaluate the ANOVA expansion of the output and freeze the least important parameter components; finally, considering a restricted model involving just the retained parameter components, we compute a second (fine) RB approximation with a smaller tolerance on the a posteriori error estimate. The fine RB approximation entails lower computational costs than the coarse one, because of the reduction of parameter dimensionality. Our result provides a criterion to avoid the computation of those terms in the ANOVA expansion that are related to the interaction between parameters in the bilinear form, thus making the RB-ANOVA-RB procedure computationally more feasible.</p>10aPartial differential equations1 aDevaud, Denis1 aManzoni, Andrea1 aRozza, Gianluigi  uhttp://hdl.handle.net/1963/7389