A Weighted Empirical Interpolation Method: A-priori Convergence Analysis and Applications

07/2013

A Weighted Empirical Interpolation Method: A-priori Convergence Analysis and Applications

Thursday 21st February 2013

Chen, P.; Quarteroni, A.; Rozza, G.

We extend the conventional empirical interpolation method to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, e.g. random variables obeying various probability distributions. A priori convergence analysis is provided for the proposed method and the error bound by Kolmogorov N-width is improved from the recent work. We apply our method to geometric Brownian motion, exponential Karhunen-Loeve expansion and reduced basis approximation of non-affine stochastic elliptic equations. We demonstrate its improved accuracy and efficiency over the empirical interpolation method, as well as sparse grid stochastic collocation method. Keywords: empirical interpolation method, a priori convergence analysis, greedy algorithm, Kolmogorov N-width, geometric Brownian motion, Karhunen-Loeve expansion, reduced basis method