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Tensor Approximation Methods for Stochastic Problems

Elmar K. Zander

ISBN 10: 3844018719 / ISBN 13: 9783844018714
Editore: Shaker Verlag Mai 2013, 2013
Nuovi Condizione: Neu
Da Rhein-Team Lörrach Ivano Narducci e.K. (Lörrach, Germania)

Libreria AbeBooks dal 11 gennaio 2012

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Neuware - Spectral stochastic methods have gained wide acceptance as a tool for efficient modelling of uncertain stochastic systems. The advantage of those methods is that they provide not only statistics, but give a direct representation of the measure of the solution as a so-called surrogate model, which can be used for very fast sampling. Especially attractive for elliptic stochastic partial differential equations (SPDEs) is the stochastic Galerkin method, since it preserves essential properties of the differential operator. One drawback of the method is, however, that it requires huge amounts of memory, as the solution is represented in a tensor product space of spatial and stochastic basis functions. Different approaches have been investigated to reduce the memory requirements, for example, model reduction techniques using subspace iterations to reduce the approximation space or methods of approximating the solution from successive rank-1 updates. In the present thesis best approximations to the solutions of linear elliptic SPDEs are constructed in low-rank tensor representations. By using tensor formats for all random quantities, the best subsets for representing the solution are computed 'on the fly' during the entire process of solving the SPDE. As those representations require additional approximations during the solution process it is essential to control the convergence of the solution. Furthermore, special issues with preconditioning of the discrete system and stagnation of the iterative methods need adequate treatment. Since one goal of this work was practical usability, special emphasis has been given to implementation techniques and their description in the necessary detail. 182 pp. Englisch. Codice inventario libreria 9783844018714

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Titolo: Tensor Approximation Methods for Stochastic ...

Casa editrice: Shaker Verlag Mai 2013

Data di pubblicazione: 2013

Legatura: Buch

Condizione libro:Neu

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