An offline/online procedure for dual norm calculations of parameterized functionals: empirical quadrature and empirical test spaces
This work provides a computational framework for efficiently evaluating parameterized functionals, which is relevant for reduced-order modeling and uncertainty quantification.
The paper develops an offline/online procedure for computing the dual norm of parameterized linear functionals, combining empirical test spaces and empirical quadrature to reduce computational costs. The method is applied to a time-averaged residual indicator, achieving significant reductions in both offline and online costs.
We present an offline/online computational procedure for computing the dual norm of parameterized linear functionals. The key elements of the approach are (i) an empirical test space for the manifold of Riesz elements associated with the parameterized functional, and (ii) an empirical quadrature procedure to efficiently deal with parametrically non-affine terms. We present a number of theoretical results to identify the different sources of error and to motivate the technique. Finally, we show the effectiveness of our approach to reduce both offline and online costs associated with the computation of the time-averaged residual indicator proposed in [Fick, Maday, Patera, Taddei, Journal of Computational Physics, 2018 (accepted)].