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arXiv · 1006.2151

A non-adapted sparse approximation of PDEs with stochastic inputs

Alireza Doostan·Houman Owhadi
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Abstract

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 (with slow decay in the spectrum).

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BibTeXRIS

Alireza Doostan, Houman Owhadi. 2010-06-10. A non-adapted sparse approximation of PDEs with stochastic inputs. https://doi.org/10.1016/j.jcp.2011.01.002

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