Abstract
We explain how to set up a RB method for problems not fulfilling the assumption of affine parametric dependence. Since the possibility to devise an offline/online decomposition relies on that assumption, in case of nonaffine problems we recover an approximate affine expansion by means of the so-called empirical interpolation method (EIM). We provide a detailed description of the EIM, focusing on linear problems for the sake of simplicity. A possible alternative formulation, referred to as discrete empirical interpolation method (DEIM), is also presented. As shown in the following chapter, EIM is an essential tool to ensure an offline/online decomposition, under suitable assumptions, also for nonlinear parametrized PDEs.
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© 2016 Springer International Publishing Switzerland
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Quarteroni, A., Manzoni, A., Negri, F. (2016). Extension to Nonaffine Problems. In: Reduced Basis Methods for Partial Differential Equations. UNITEXT(), vol 92. Springer, Cham. https://doi.org/10.1007/978-3-319-15431-2_10
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DOI: https://doi.org/10.1007/978-3-319-15431-2_10
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-15430-5
Online ISBN: 978-3-319-15431-2
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