Tensor product methods for stochastic problems

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)