Combining metamodels with rational function representations of discretization error for uncertainty quantification Original Research Article

Techniques for producing metamodels for the efficient 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 significantly affect 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 significant savings.