A non-adapted sparse approximation of PDEs with stochastic inputs

作者：Doostan Alireza^*; Owhadi Houman

来源：Journal of Computational Physics, 2011, 230(8): 3015-3034.

DOI：10.1016/j.jcp.2011.01.002

• Polynomial chaos
• Uncertainty quantification
• Stochastic PDE
• Compressive sampling
• Sparse approximation

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.

• 出版日期2011-4-20