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.
Read the Original
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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