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Normal Hyperbolicity of Manifolds of Equilibria in Nonlinear Circuits with Mem-Devices Read chapter Read first chapter

2014 | OriginalPaper | Chapter

Efficient Calculation of Uncertainty Quantification

Authors : E. Jan W. ter Maten, Roland Pulch, Wil H. A. Schilders, H. H. J. M. Janssen

Published in: Progress in Industrial Mathematics at ECMI 2012

Publisher: Springer International Publishing

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Abstract

We consider Uncertainty Quantification (UQ) by expanding the solution in so-called generalized Polynomial Chaos expansions. In these expansions the solution is decomposed into a series with orthogonal polynomials in which the parameter dependency becomes an argument of the orthogonal polynomial basis functions. The time and space dependency remains in the coefficients. In UQ two main approaches are in use: Stochastic Collocation (SC) and Stochastic Galerkin (SG). Practice shows that in many cases SC is more efficient for similar accuracy as obtained by SG. In SC the coefficients in the expansion are approximated by quadrature and thus lead to a large series of deterministic simulations for several parameters. We consider strategies to efficiently perform this sequence of deterministic simulations within SC.

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previous chapter Polynomial-Chaos Based Methods for Differential Algebraic Equations with Random Parameters
next chapter A Stochastic Geometric Framework for Dynamical Birth-and-Growth Processes: Related Statistical Analysis
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Metadata
Title
Efficient Calculation of Uncertainty Quantification
Authors
E. Jan W. ter Maten
Roland Pulch
Wil H. A. Schilders
H. H. J. M. Janssen
Copyright Year
2014
Book
Progress in Industrial Mathematics at ECMI 2012

Print ISBN: 978-3-319-05364-6

Electronic ISBN: 978-3-319-05365-3

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-05365-3_50

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