Analysis and Applications of an Anisotropic Sparse Grid Stochastic Collocation Technique for PDEs with Random Input Data
Abstract not provided.
Publications
Evaluation of Non-Intrusive Approaches for Wiener-Askey Generalized Polynomial Chaos
Abstract not provided.
The analysis of a sparse grid stochastic collocation method for partial differential equations with high-dimensional random input data
This work describes the convergence analysis of a Smolyak-type sparse grid stochastic collocation method for the approximation of statistical quantities related to the solution of partial differential equations with random coefficients and forcing terms (input data of the model). To compute solution statistics, the sparse grid stochastic collocation method uses approximate solutions, produced here by finite elements, corresponding to a deterministic set of points in the random input space. This naturally requires solving uncoupled deterministic problems and, as such, the derived strong error estimates for the fully discrete solution are used to compare the computational efficiency of the proposed method with the Monte Carlo method. Numerical examples illustrate the theoretical results and are used to compare this approach with several others, including the standard Monte Carlo.
Analyzing Sparse-Grid UQ Techniques for Verification within Predictive Science
Abstract not provided.
4 Results