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A Preconditioner for Fictitious Domain Formulations of Elliptic PDEs on Uncertain Parameterized Domains

Gordon, Andrew; Powell, Catherine

2014;2(1):622-645.

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Abstract

We consider the numerical solution of elliptic boundary-value problems on uncertain two-dimensional domains via the fictitious domain method. This leads to variational problems of saddle point form. Working under the standard assumption that the domain can be described by a finite number of independent random variables, discretization is achieved by a stochastic collocation mixed finite element method. We focus on the efficient iterative solution of the resulting sequence of indefinite linear systems and introduce a novel and efficient preconditioner for use with the minimal residual method. The challenging task is to construct a matrix that provides a robust approximation to a discrete representation of a trace space norm on a parameterized boundary.

Bibliographic metadata

Type of resource:
Content type:
Publication status:
Accepted
Publication type:
Publication form:
Published date:
ISSN:
Publisher:
Publishers website:
http://epubs.siam.org/doi/abs/10.1137/130924202
Volume:
2
Issue:
1
Start page:
622
End page:
645
Total:
23
Pagination:
622-645
Digital Object Identifier:
10.1137/130924202
Funding awarded to University:
  • EPSRC - RESEPSRC
Funding awarded externally:
Attached files embargo period:
Immediate release
Attached files release date:
3rd December, 2014
Access state:
Active

Institutional metadata

University researcher(s):

Record metadata

Manchester eScholar ID:
uk-ac-man-scw:241880
Created by:
Powell, Catherine
Created:
3rd December, 2014, 15:25:32
Last modified by:
Powell, Catherine
Last modified:
3rd December, 2014, 15:25:32

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