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Stochastic projection schemes for deterministic linear elliptic partial differential equations on random domains

Record type: Article

We present stochastic projection schemes for approximating the solution of a class of deterministic linear elliptic partial differential equations defined on random domains. The key idea is to carry out spatial discretization using a combination of finite element methods and stochastic mesh representations. We prove a result to establish the conditions that the input uncertainty model must satisfy to ensure the validity of the stochastic mesh representation and hence the well posedness of the problem. Finite element spatial discretization of the governing equations using a stochastic mesh representation results in a linear random algebraic system of equations in a polynomial chaos basis whose coefficients of expansion can be non-intrusively computed either at the element or the global level. The resulting randomly parametrized algebraic equations are solved using stochastic projection schemes to approximate the response statistics. The proposed approach is demonstrated for modeling diffusion in a square domain with a rough wall and heat transfer analysis of a three-dimensional gas turbine blade model with uncertainty in the cooling core geometry. The numerical results are compared against Monte–Carlo simulations, and it is shown that the proposed approach provides high-quality approximations for the first two statistical moments at modest computational effort.

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Citation

Mohan, P. Surya, Nair, Prasanth B. and Keane, Andy J. (2011) Stochastic projection schemes for deterministic linear elliptic partial differential equations on random domains International Journal for Numerical Methods in Engineering, 85, (7), pp. 874-895. (doi:10.1002/nme.3004).

More information

e-pub ahead of print date: 23 August 2010
Published date: 18 February 2011
Organisations: Computational Engineering & Design Group

Identifiers

Local EPrints ID: 204239
URI: http://eprints.soton.ac.uk/id/eprint/204239
ISSN: 0029-5981
PURE UUID: 8871796a-bd83-4cc0-924d-c9d5ebbd66bc

Catalogue record

Date deposited: 25 Nov 2011 14:07
Last modified: 18 Jul 2017 11:06

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Contributors

Author: P. Surya Mohan
Author: Prasanth B. Nair
Author: Andy J. Keane

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