Tensor product methods for stochastic problems |
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Authors: | Elmar Zander H. G. Matthies |
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Affiliation: | TU Braunschweig, Institut für Wissenschaftliches Rechnen, Hans-Sommer-Str. 65, 38106 Braunschweig, Germany |
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Abstract: | In the solution of stochastic partial differential equations (SPDEs) the generally already large dimension N of the algebraic system resulting from the spatial part of the problem is blown up by the huge number of degrees of freedom P coming from the stochastic part. The number of degrees of freedom of the full system will be NP, which poses severe demands on memory and processor time. We present a method how to approximate the system by a data-sparse tensor product (based on the Karhunen-Loève decomposition with M terms), which uses only memory in the order of M (N + P), and how to keep this representation also inside the iterative solvers. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) |
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