Accession Number:

ADA458984

Title:

An Adaptive Multi-Element Generalized Polynomial Chaos Method for Stochastic Differential Equations

Descriptive Note:

Journal article preprint

Corporate Author:

BROWN UNIV PROVIDENCE RI DIV OF APPLIED MATHEMATICS

Report Date:

2005-03-09

Pagination or Media Count:

32.0

Abstract:

We formulate a Multi-Element generalized Polynomial Chaos ME-gPC method to deal with long-term integration and discontinuities in stochastic diffierential equations. We first present this method for Legendre-chaos corresponding to uniform random inputs, and subsequently we generalize it to other random inputs. The main idea of ME-gPC is to decompose the space of random inputs when the relative error in variance becomes greater than a threshold value. In each subdomain or random element, we then employ a generalized Polynomial Chaos expansion. We develop a criterion to perform such a decomposition adaptively, and demonstrate its effectiveness for ODEs, including the Kraichnan-Orszag three-mode problem, as well as advection-diffusion problems. The new method is similar to spectral element method for deterministic problems but with h-p discretization of the random space.

Subject Categories:

  • Theoretical Mathematics
  • Operations Research

Distribution Statement:

APPROVED FOR PUBLIC RELEASE