Approximation of the stochastic Galerkin matrix in the low‐rank canonical tensor format

Abstract

AbstractIn this article we describe an efficient approximation of the stochastic Galerkin matrix which stems from a stationary diffusion equation. The uncertain permeability coefficient is assumed to be a log‐normal random field with given covariance and mean functions. The approximation is done in the canonical tensor format and then compared numerically with the tensor train and hierarchical tensor formats. It will be shown that under additional assumptions the approximation error depends only on smoothness of the covariance function and does not depend either on the number of random variables nor the degree of the multivariate Hermite polynomials. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)