Skip to main content
U.S. Department of Energy
Office of Scientific and Technical Information

A multilevel stochastic collocation method for SPDEs

Journal Article · · AIP Conference Proceedings
DOI:https://doi.org/10.1063/1.4912309· OSTI ID:22391036
 [1];  [2];  [1];  [3]
  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, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 1648; ISSN APCPCS; ISSN 0094-243X
Country of Publication:
United States
Language:
English