What is it about?

We consider an elliptic PDE with uncertain diffusion coefficient. This is a highly - dimensional problem, and usual methods either do not work or very slow. To solve it we compute a tensor approximation of the stochastic Galerkin operator. Tensor ranks of the solution depend on the tensor ranks of the Galerkin operator. Particularly, we show that tensor ranks of the Galerkin operator are independent from the number of used PCE coefficients.

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Why is it important?

Sharp estimates of tensor ranks will help to develop efficient numerical methods for solving high-dimensional problems.

Perspectives

Two experienced groups were involved in this project. The first one is the tensor group and the second is the uncertainty quantification group. Both groups learned a lot from each other. The developed methods and estimates are main steps for high-dimensional data analysis.

Dr. Alexander Litvinenko
Rheinisch Westfalische Technische Hochschule Aachen

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This page is a summary of: Efficient low-rank approximation of the stochastic Galerkin matrix in tensor formats, Computers & Mathematics with Applications, March 2014, Elsevier, DOI: 10.1016/j.camwa.2012.10.008.
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