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Polynomial chaos for the approximation of uncertainties: Chances and limits

Published online by Cambridge University Press:  01 April 2008

F. AUGUSTIN ,
A. GILG ,
M. PAFFRATH ,
P. RENTROP  and
U. WEVER
F. AUGUSTIN
Affiliation:
Technical University of Munich, Department of Mathematics, 85748 Garching, Germany email: augustin@ma.tum.de; toth-pinter@ma.tum.de
A. GILG
Affiliation:
Siemens AG, Corporate Technology, Otto-Hahn-Ring 6, 81730 Munich, Germany email: albert.gilg@siemens.com; meinhard.paffrath@siemens.com; utz.wever@siemens.com
M. PAFFRATH
Affiliation:
Siemens AG, Corporate Technology, Otto-Hahn-Ring 6, 81730 Munich, Germany email: albert.gilg@siemens.com; meinhard.paffrath@siemens.com; utz.wever@siemens.com
P. RENTROP
Affiliation:
Technical University of Munich, Department of Mathematics, 85748 Garching, Germany email: augustin@ma.tum.de; toth-pinter@ma.tum.de
U. WEVER
Affiliation:
Siemens AG, Corporate Technology, Otto-Hahn-Ring 6, 81730 Munich, Germany email: albert.gilg@siemens.com; meinhard.paffrath@siemens.com; utz.wever@siemens.com
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Abstract

In technical applications, uncertainties are a topic of increasing interest. During the last years the Polynomial Chaos of Wiener (Amer. J. Math. 60(4), 897–936, 1938) was revealed to be a cheap alternative to Monte Carlo simulations. In this paper we apply Polynomial Chaos to stationary and transient problems, both from academics and from industry. For each of the applications, chances and limits of Polynomial Chaos are discussed. The presented problems show the need for new theoretical results.

Type
A Survey in Mathematics for Industry
Information
European Journal of Applied Mathematics , Volume 19 , Issue 2 , April 2008 , pp. 149 - 190
Copyright
Copyright © Cambridge University Press 2008

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