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Title: A multilevel stochastic collocation method for SPDEs

Abstract

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.

Authors:
 [1];  [2];  [1];  [3]
  1. Florida State University (United States)
  2. University of Tennessee (United States)
  3. Oak Ridge National Laboratory (United States)
Publication Date:
OSTI Identifier:
22391036
Resource Type:
Journal Article
Journal Name:
AIP Conference Proceedings
Additional Journal Information:
Journal Volume: 1648; Journal 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); Journal ID: ISSN 0094-243X
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; COMPARATIVE EVALUATIONS; CONVERGENCE; MONTE CARLO METHOD; PARTIAL DIFFERENTIAL EQUATIONS; RANDOMNESS; SPACE; STOCHASTIC PROCESSES

Citation Formats

Gunzburger, Max, Jantsch, Peter, Teckentrup, Aretha, and Webster, Clayton. A multilevel stochastic collocation method for SPDEs. United States: N. p., 2015. Web. doi:10.1063/1.4912309.
Gunzburger, Max, Jantsch, Peter, Teckentrup, Aretha, & Webster, Clayton. A multilevel stochastic collocation method for SPDEs. United States. https://doi.org/10.1063/1.4912309
Gunzburger, Max, Jantsch, Peter, Teckentrup, Aretha, and Webster, Clayton. 2015. "A multilevel stochastic collocation method for SPDEs". United States. https://doi.org/10.1063/1.4912309.
@article{osti_22391036,
title = {A multilevel stochastic collocation method for SPDEs},
author = {Gunzburger, Max and Jantsch, Peter and Teckentrup, Aretha and Webster, Clayton},
abstractNote = {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.},
doi = {10.1063/1.4912309},
url = {https://www.osti.gov/biblio/22391036}, journal = {AIP Conference Proceedings},
issn = {0094-243X},
number = 1,
volume = 1648,
place = {United States},
year = {Tue Mar 10 00:00:00 EDT 2015},
month = {Tue Mar 10 00:00:00 EDT 2015}
}