Abstract
As discussed previously, the computational efficiency of the reduced basis method relies strongly on the affine assumption , i.e., we generally assume that \(a(w,v;\mu ) = \sum _{q = 1}^{{Q_\mathtt{a}}} \theta _\mathtt{a}^q(\mu ) \, a_q(w,v), \qquad \forall w,v \in \mathbb V, \, \forall \mu \in \mathbb P\), and similarly for the righthand side and the output of interest. Unfortunately, this assumption fails for the majority of problems one would like to consider and it is essential to look for ways to overcome this assumption by approximating the non-affine elements in a suitable way.
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Hesthaven, J.S., Rozza, G., Stamm, B. (2016). The Empirical Interpolation Method. In: Certified Reduced Basis Methods for Parametrized Partial Differential Equations. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-22470-1_5
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