Issue No. 03 - May/June (2005 vol. 7)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/MCSE.2005.46
Dongbin Xiu , Princeton University
Ioannis G. Kevrekidis , Princeton University
Roger Ghanem , University of Southern California
Recently, interest has grown in developing efficient computational methods (both sampling and nonsampling) for studying ordinary or partial differential equations with random inputs. Stochastic Galerkin (SG) methods based on generalized polynomial chaos (gPC) representations have several appealing features. However, when the model equations are complicated, the numerical implementation of such algorithms can become highly nontrivial, and care is needed to design robust and efficient solvers for the resulting systems of equations. The authors' equation- and Galerkin-free computational approach to uncertainty quantification (UQ) for dynamical systems lets them conduct UQ computations without explicitly deriving the SG equations for the gPC coefficients. They use short bursts of appropriately initialized ensembles of simulations with the basic model to estimate the quantities required in SG algorithms.
uncertainty quantification, stochastic Galerkin methods, generalized polynomial chaos, equation-free computation, projective integration
R. Ghanem, D. Xiu and I. G. Kevrekidis, "An Equation-Free, Multiscale Approach to Uncertainty Quantification," in Computing in Science & Engineering, vol. 7, no. , pp. 16-23, 2005.