A multilevel stochastic collocation method for SPDEs

Journal Article · Tue Mar 10 00:00:00 EDT 2015 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.4912309· OSTI ID:22391036

Gunzburger, Max ^[1]; Jantsch, Peter ^[2]; Teckentrup, Aretha ^[1]; Webster, Clayton ^[3]

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1. Florida State University (United States)
2. University of Tennessee (United States)
3. Oak Ridge National Laboratory (United States)

We present a multilevel stochastic collocation method that, as do multilevel Monte Carlo methods, uses a hierarchy of spatial approximations to reduce the overall computational complexity when solving partial differential equations with random inputs. For approximation in parameter space, a hierarchy of multi-dimensional interpolants of increasing fidelity are used. Rigorous convergence and computational cost estimates for the new multilevel stochastic collocation method are derived and used to demonstrate its advantages compared to standard single-level stochastic collocation approximations as well as multilevel Monte Carlo methods.

• OSTI ID: 22391036
• Journal Information: AIP Conference Proceedings, Vol. 1648, Issue 1; Conference: ICNAAM-2014: International Conference on Numerical Analysis and Applied Mathematics 2014, Rhodes (Greece), 22-28 Sep 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
COMPARATIVE EVALUATIONS
CONVERGENCE
MONTE CARLO METHOD
PARTIAL DIFFERENTIAL EQUATIONS
RANDOMNESS
SPACE
STOCHASTIC PROCESSES