An adaptive wavelet stochastic collocation method for irregular solutions of stochastic partial differential equations

Webster, Clayton G ; Zhang, Guannan ; Gunzburger, Max D

Oak Ridge National Laboratory

关键词: Uncertainty Quantification;    Collocation Techniques;    Stochastic Pdes;    Adaptive Sparse Grids;    High-Dimensional Approximation;   

DOI  :  10.2172/1081925
RP-ID  :  ORNL/TM-2012/186
RP-ID  :  DE-AC05-00OR22725
RP-ID  :  1081925

美国|英语

来源: UNT Digital Library

【 摘 要 】

Accurate predictive simulations of complex real world applications require numerical approximations to first, oppose the curse of dimensionality and second, converge quickly in the presence of steep gradients, sharp transitions, bifurcations or finite discontinuities in high-dimensional parameter spaces. In this paper we present a novel multi-dimensional multi-resolution adaptive (MdMrA) sparse grid stochastic collocation method, that utilizes hierarchical multiscale piecewise Riesz basis functions constructed from interpolating wavelets. The basis for our non-intrusive method forms a stable multiscale splitting and thus, optimal adaptation is achieved. Error estimates and numerical examples will used to compare the efficiency of the method with several other techniques.