SPARE—A Scalable Algorithm for Passive, Structure Preserving, Parameter-Aware Model Order Reduction

Stochastic Galerkin Methods and Model Order Reduction for Linear Dynamical Systems

“…For increasing M , the integrand of the upper bound converges point-wise to zero for each t ≥ 0 due to (15). We obtain the convergence (16) by the theorem of dominated convergence.…”

“…i.e., the sequence y (M ) (t, p) of outputs satisfies (15). Under the additional assumptions of Lemma 1, it follows that…”

“…Alternatively, techniques of parameterized model order reduction (pMOR) preserve the parameters as independent variables in reduced systems, see [12,14,15,30]. Often constant projection matrices W 0 , V 0 ∈ C N ×N red are determined a priori using the information from many samples of the parameters, cf.…”

“…Appropriate MOR methods are available for linear dynamical systems, see [9][10][11]. Moreover, parameterized model order reduction (pMOR) has been developed to preserve deterministic parameters as independent variables in the reduced order models, see [12][13][14][15]. In case of large numbers of random parameters, a reduction of the random space based on a sensitivity analysis is discussed in [16].…”

Sensitivity analysis and model order reduction for random linear dynamical systems

“…Parametric model order reduction (pMOR) yields reduced systems (18), where the parameters p still appear as independent variables, see [4,6,25]. Consequently, the computational effort becomes lower in a nonintrusive method for random parameters.…”