Mathematical Foundations for the Analysis and Simulation of Stochastic PDEs

Clayton Webster, John von Neumann Fellow FY2008-2009

My UQ efforts are focused on generating novel, efficient and reliable Stochastic techniques for solving complex PDE systems with large amounts of uncertain input information

• Large amounts of uncertainty lead to extremely high-dimensional statistical approximations
• Algorithm development has employed both Intrusive and Non-intrusive (NI) Stochastic FEMs.
• The dominant NI approach is based on Stochastic Collocation FEMs, including: Adaptive Tensor Products, Sparse Grids (SG) and Dimension-Adaptive SG

Our UQ efforts have reduced computation time by ORDERs of magnitude

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