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

Technical Report · Mon Oct 01 00:00:00 EDT 2012

DOI:https://doi.org/10.2172/1081925· OSTI ID:1081925

Webster, Clayton G ^[1]; Zhang, Guannan ^[1]; Gunzburger, Max D ^[1]

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1. ORNL

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.

• Research Organization: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE Laboratory Directed Research and Development (LDRD) Program
• DOE Contract Number: DE-AC05-00OR22725
• OSTI ID: 1081925
• Report Number(s): ORNL/TM-2012/186
• Country of Publication: United States
• Language: English

Related Subjects

multi-dimensional multi-resolution analysis
wavelet basis
stochastic PDEs
collocation techniques
adaptive sparse grids
uncertainty quantification
high-dimensional approximation
best N-term approximation