Approximation of the stochastic Galerkin matrix in the low-rank canonical tensor format
Corresponding Author
Philipp Wähnert
Max-Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany
Philipp Wähnert, phone +49 341 9959 773, fax +49 341 9959 999
Alexander Litvinenko, phone +49 531 391 3008, fax +49 531 391 3003
Mike Espig, phone +49 341 9959 780, fax +49 341 9959 999
Hermann G. Matthies, phone +49 531 391 3000, fax +49 531 391 3003
Wolfgang Hackbusch, phone +49 341 9959 750, fax +49 341 9959 999
Search for more papers by this authorCorresponding Author
Alexander Litvinenko
Technische Universität Braunschweig, Hans-Sommerstr. 65, Braunschweig 38106
Philipp Wähnert, phone +49 341 9959 773, fax +49 341 9959 999
Alexander Litvinenko, phone +49 531 391 3008, fax +49 531 391 3003
Mike Espig, phone +49 341 9959 780, fax +49 341 9959 999
Hermann G. Matthies, phone +49 531 391 3000, fax +49 531 391 3003
Wolfgang Hackbusch, phone +49 341 9959 750, fax +49 341 9959 999
Search for more papers by this authorCorresponding Author
Mike Espig
Max-Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany
Philipp Wähnert, phone +49 341 9959 773, fax +49 341 9959 999
Alexander Litvinenko, phone +49 531 391 3008, fax +49 531 391 3003
Mike Espig, phone +49 341 9959 780, fax +49 341 9959 999
Hermann G. Matthies, phone +49 531 391 3000, fax +49 531 391 3003
Wolfgang Hackbusch, phone +49 341 9959 750, fax +49 341 9959 999
Search for more papers by this authorCorresponding Author
Hermann G. Matthies
Technische Universität Braunschweig, Hans-Sommerstr. 65, Braunschweig 38106
Philipp Wähnert, phone +49 341 9959 773, fax +49 341 9959 999
Alexander Litvinenko, phone +49 531 391 3008, fax +49 531 391 3003
Mike Espig, phone +49 341 9959 780, fax +49 341 9959 999
Hermann G. Matthies, phone +49 531 391 3000, fax +49 531 391 3003
Wolfgang Hackbusch, phone +49 341 9959 750, fax +49 341 9959 999
Search for more papers by this authorCorresponding Author
Wolfgang Hackbusch
Max-Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany
Philipp Wähnert, phone +49 341 9959 773, fax +49 341 9959 999
Alexander Litvinenko, phone +49 531 391 3008, fax +49 531 391 3003
Mike Espig, phone +49 341 9959 780, fax +49 341 9959 999
Hermann G. Matthies, phone +49 531 391 3000, fax +49 531 391 3003
Wolfgang Hackbusch, phone +49 341 9959 750, fax +49 341 9959 999
Search for more papers by this authorCorresponding Author
Philipp Wähnert
Max-Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany
Philipp Wähnert, phone +49 341 9959 773, fax +49 341 9959 999
Alexander Litvinenko, phone +49 531 391 3008, fax +49 531 391 3003
Mike Espig, phone +49 341 9959 780, fax +49 341 9959 999
Hermann G. Matthies, phone +49 531 391 3000, fax +49 531 391 3003
Wolfgang Hackbusch, phone +49 341 9959 750, fax +49 341 9959 999
Search for more papers by this authorCorresponding Author
Alexander Litvinenko
Technische Universität Braunschweig, Hans-Sommerstr. 65, Braunschweig 38106
Philipp Wähnert, phone +49 341 9959 773, fax +49 341 9959 999
Alexander Litvinenko, phone +49 531 391 3008, fax +49 531 391 3003
Mike Espig, phone +49 341 9959 780, fax +49 341 9959 999
Hermann G. Matthies, phone +49 531 391 3000, fax +49 531 391 3003
Wolfgang Hackbusch, phone +49 341 9959 750, fax +49 341 9959 999
Search for more papers by this authorCorresponding Author
Mike Espig
Max-Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany
Philipp Wähnert, phone +49 341 9959 773, fax +49 341 9959 999
Alexander Litvinenko, phone +49 531 391 3008, fax +49 531 391 3003
Mike Espig, phone +49 341 9959 780, fax +49 341 9959 999
Hermann G. Matthies, phone +49 531 391 3000, fax +49 531 391 3003
Wolfgang Hackbusch, phone +49 341 9959 750, fax +49 341 9959 999
Search for more papers by this authorCorresponding Author
Hermann G. Matthies
Technische Universität Braunschweig, Hans-Sommerstr. 65, Braunschweig 38106
Philipp Wähnert, phone +49 341 9959 773, fax +49 341 9959 999
Alexander Litvinenko, phone +49 531 391 3008, fax +49 531 391 3003
Mike Espig, phone +49 341 9959 780, fax +49 341 9959 999
Hermann G. Matthies, phone +49 531 391 3000, fax +49 531 391 3003
Wolfgang Hackbusch, phone +49 341 9959 750, fax +49 341 9959 999
Search for more papers by this authorCorresponding Author
Wolfgang Hackbusch
Max-Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany
Philipp Wähnert, phone +49 341 9959 773, fax +49 341 9959 999
Alexander Litvinenko, phone +49 531 391 3008, fax +49 531 391 3003
Mike Espig, phone +49 341 9959 780, fax +49 341 9959 999
Hermann G. Matthies, phone +49 531 391 3000, fax +49 531 391 3003
Wolfgang Hackbusch, phone +49 341 9959 750, fax +49 341 9959 999
Search for more papers by this authorAbstract
In 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)
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