Article in Journal ART-2003-06

BibliographyBungartz, Hans-Joachim; Dirnstorfer, Stefan: Multivariate quadrature on adaptive sparse grids.
In: Computing. Vol. 71(1).
University of Stuttgart, Faculty of Computer Science, Electrical Engineering, and Information Technology.
pp. 89-114, english.
New York: Springer, September 2003.
ISBN: 0010-485X.
Article in Journal.
CR-SchemaG.1 (Numerical Analysis)
I.1 (Symbolic and Algebraic Manipulation)
Abstract

In this paper, we study the potential of adaptive sparse grids for multivariate numerical quadrature in the moderate or high dimensional case, i.e. for a number of dimensions beyond three and up to several hundreds. There, conventional methods typically suffer from the curse of dimension or are unsatisfactory with respect to accuracy. Our sparse grid approach, based upon a direct higher order discretization on the sparse grid, overcomes this dilemma to some extent, and introduces additional flexibility with respect to both the order of the 1 D quadrature rule applied (in the sense of Smolyak's tensor product decomposition) and the placement of grid points. The presented algorithm is applied to some test problems and compared with other existing methods.

Department(s)University of Stuttgart, Institute of Parallel and Distributed Systems, Simulation of Large Systems
Entry dateOctober 22, 2004
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