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

Code:
07/2013
Title:
A Weighted Empirical Interpolation Method: A-priori Convergence Analysis and Applications
Date:
Thursday 21st February 2013
Author(s):
Chen, P.; Quarteroni, A.; Rozza, G.
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Abstract:
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