A multilevel stochastic collocation method for SPDEs

Max Gunzburger, Peter Jantsch, Aretha Teckentrup, Clayton Webster

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish
Title of host publicationProceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014
PublisherAmerican Institute of Physics Inc.
Number of pages3
Volume1648
ISBN (Print)9780735412873
DOIs
Publication statusPublished - Apr 2015
EventInternational Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014 - Rhodes, Greece
Duration: 22 Sep 201428 Sep 2014

Conference

ConferenceInternational Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014
CountryGreece
CityRhodes
Period22/09/1428/09/14

Keywords

  • finite element methods
  • multilevel methods
  • SPDEs
  • stochastic collocation
  • uncertainty quantification

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