MULTILEVEL ACCELERATION OF STOCHASTIC COLLOCATION METHODS FOR PDE WITH RANDOM INPUT DATA

Journal Article · Tue Jan 01 00:00:00 EST 2013 · SIAM Journal on Uncertainty Quantification

OSTI ID:1096366

Webster, Clayton G ^[1]; Jantsch, Peter A ^[1]; Teckentrup, Aretha L ^[1]; Gunzburger, Max D ^[1]

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1. ORNL

Stochastic Collocation (SC) methods for stochastic partial differential equa- tions (SPDEs) suffer from the curse of dimensionality, whereby increases in the stochastic dimension cause an explosion of computational effort. To combat these challenges, multilevel approximation methods seek to decrease computational complexity by balancing spatial and stochastic discretization errors. As a form of variance reduction, multilevel techniques have been successfully applied to Monte Carlo (MC) methods, but may be extended to accelerate other methods for SPDEs in which the stochastic and spatial degrees of freedom are de- coupled. This article presents general convergence and computational complexity analysis of a multilevel method for SPDEs, demonstrating its advantages with regard to standard, single level approximation. The numerical results will highlight conditions under which multilevel sparse grid SC is preferable to the more traditional MC and SC approaches.

• 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: 1096366
• Journal Information: SIAM Journal on Uncertainty Quantification, Journal Name: SIAM Journal on Uncertainty Quantification
• Country of Publication: United States
• Language: English