A multilevel sparse kernel-based stochastic collocation finite element method for elliptic problems with random coefficients.pdf (555.05 kB)
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A multilevel sparse kernel-based stochastic collocation finite element method for elliptic problems with random coefficients

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journal contribution
posted on 07.09.2018, 14:42 by Zhaonan Dong, Emmanuil H. Georgoulis, Jeremy Levesley, Fuat Usta
A new stochastic collocation finite element method is proposed for the numerical solution of elliptic boundary value problems (BVP) with random coefficients, assuming that the randomness is well-approximated by a finite number of random variables with given probability distributions. The proposed method consists of a finite element approximation in physical space, along with a stochastic collocation quadrature approach utilizing the recent Multilevel Sparse Kernel-Based Interpolation (MuSIK) technique (Georgoulis et al., 2013). MuSIK is based on a multilevel sparse grid-type algorithm with the basis functions consisting of directionally anisotropic Gaussian radial basis functions (kernels) placed at directionally-uniform grid-points. We prove that MuSIK is interpolatory at these nodes, and, therefore, can be naturally used to define a quadrature scheme. Numerical examples are also presented, assessing the performance of the new algorithm in the context of high-dimensional stochastic collocation finite element methods.

History

Citation

Computers and Mathematics with Applications, 2018

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

AM (Accepted Manuscript)

Published in

Computers and Mathematics with Applications

Publisher

Elsevier

issn

0898-1221

Acceptance date

29/07/2018

Copyright date

2018

Available date

23/08/2019

Publisher version

https://www.sciencedirect.com/science/article/pii/S0898122118304127?via=ihub

Notes

The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.

Language

en