An Adaptive Wavelet Stochastic Collocation Method for Irregular Solutions of Stochastic Partial Differential Equations

Technical Report · Sat Sep 01 04:00:00 EDT 2012

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

Gunzburger, Max D. ^[1]; Webster, Clayton G. ^[2]; Zhang, Guannan ^[2]

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1. Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States); Florida State Univ., Tallahassee, FL (United States)
2. Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

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 Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); US Air Force Office of Scientific Research (AFOSR)
• DOE Contract Number: AC05-00OR22725
• OSTI ID: 1081925
• Report Number(s): ORNL/TM--2012/186
• Country of Publication: United States
• Language: English

Related Subjects

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