Time-Dependent Polynomial Chaos

Master thesis (2006)

Authors

Contributors

M.I. Gerritsma (mentor)
Faculty
Aerospace Engineering (Aerospace Engineering) (TU Delft)
Copyright: © Delft University of Technology
Uncertainty Polynomial chaos Long-term integration Stochastic ODE
More Info
expand_more

Published Date

18-10-2006

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Aerospace Engineering

Abstract

Generalized polynomial chaos is known to fail for long-term integration, loosing its optimal convergence behavior and developing unacceptable error-levels. In this work, we present a time-dependent alternative of polynomial chaos in order to overcome these issues. This technique exists out of an on-the-fly reinitialization of the polynomial chaos expansion at different discrete time-levels. At those time-levels, the new polynomial chaos expansion will be created in terms of the stochastic solution. This time-dependent approach is applied on a stochastic ODE of which the results are compared with a standard gPC solution.