The second contribution is a post-processing algorithm for computing quantities of interest at the wall that achieves smoothness in the computed solution and its gradients.
The following subsection explains the first two differences and highlights how SParSE achieves the same time complexity as dwSSA for computing quantities in (i).
The algorithm for computing these quantities is taken directly from the evaluation program treating the measurement signals.
The DDM method is well known for computing response quantities with high level of accuracy (Kleiber et al. 1997; Arora and Haug 1979; Zhang and Der Kiureghian 1993).
We also show that the numerical method of Wang, Peskin, Elston (WPE, 2003) for computing said quantities is equivalent to that resulting from homogenization theory.
There is a number of different methods for computing this quantities in the literature (Hernández-Lemus and Rangel-Escareño 2011) and most of them are quite functional and almost equivalent in performance.
In addition, they supply unambiguous quantitative definitions of terms such as margins, epistemic and aleatoric uncertainties, verification and validation measures, confidence factors, and others, as well as providing clear procedures for computing these quantities by means of concerted simulation and experimental campaigns.
Furthermore, even in the stochastic case, the model predictive control method can give ex ante suboptimal results if a finite horizon problem starting in period t has a time horizon too short for computing ordered quantities in all periods t,…,r t. (Compare the last sentence in the first paragraph of Remark 5).
Implementations of efficient algorithms for computing these quantities are available online [ 33].
Recently the authors in [6] gave the center variety for families of p : − q resonant polynomial vector fields, and moreover derived an algorithm for computing the focus quantities.
