A non-adapted sparse approximation of PDEs with stochastic inputs
We propose a method for the approximation of solutions of PDEs with stochastic coefficients based on the direct, i.e., non-adapted, sampling of solutions. This sampling can be done by using any legacy code for the deterministic problem as a black box. The method converges in probability (with probabilistic error bounds) as a consequence of sparsity and a concentration of measure phenomenon on the empirical correlation between samples. We show that the method is well suited for truly high-dimensional problems. (C) 2011 Elsevier Inc. All rights reserved.
sparse approximation polynomial chaos uncertainty quantification stochastic pde compressive sampling