Combining metamodels with rational function representations of discretization error for uncertainty quantification
✍ Scribed by Daniel C. Kammer; Kenneth F. Alvin; David S. Malkus
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 144 KB
- Volume
- 191
- Category
- Article
- ISSN
- 0045-7825
No coin nor oath required. For personal study only.
✦ Synopsis
Techniques for producing metamodels for the ecient Monte Carlo simulation of high consequence systems are presented. The bias of f.e.m mesh discretization errors is eliminated or minimized by extrapolation, using rational functions, rather than the power series representation of Richardson extrapolation. Examples, including estimation of the vibrational frequency of a one-dimensional bar, show that the rational function model gives more accurate estimates using fewer terms than Richardson extrapolation, an important consideration for computational reliability assessment of high-consequence systems, where small biases in solutions can signi®cantly aect the accuracy of small-magnitude probability estimates. Rational function representation of discretization error enable the user to accurately extrapolate to the continuum from numerical experiments performed outside the asymptotic region of the usual power series, allowing use of coarser meshes in the numerical experiments, resulting in signi®cant savings.