Tensor product methods for stochastic problems | Zendy

Zander Elmar | Zendy; Matthies H. G. | Zendy

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Tensor product methods for stochastic problems

Author(s) -

Zander Elmar,

Matthies H. G.

Publication year - 2007

Publication title -

pamm

Language(s) - English

Resource type - Journals

ISSN - 1617-7061

DOI - 10.1002/pamm.200700773

Subject(s) - tensor product , degrees of freedom (physics and chemistry) , dimension (graph theory) , tensor (intrinsic definition) , algebraic number , decomposition , representation (politics) , product (mathematics) , mathematics , algebraic equation , algebra over a field , computer science , pure mathematics , mathematical analysis , physics , geometry , ecology , quantum mechanics , politics , political science , law , biology , nonlinear system

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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