Extension to nonaffine problems

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.