Multi-element stochastic reduced basis methods
Multi-element stochastic reduced basis methods
This paper presents mutli-element Stochastic Reduced Basis Methods (ME-SRBMs) for solving linear stochastic partial differential equations. In ME-SRBMs, the domain of definition of the random inputs is decomposed into smaller subdomains or random elements. Stochastic Reduced Basis Methods (SRBMs) are employed in each random element to evaluated the response statistics. These elemental statistics are assimilated to compute the overall statistics. The effectiveness of the method is demonstrated by solving the stochastic steady state heat transfer equation on two geometries involving different types of boundary conditions. Numerical studies are conducted to investigate the h-convergence rates of global and local preconditioning strategies.
stochastic reduced basis methods, stochastic partial differential equations, uncertainty quantification, heat transfer, preconditioning
1495-1506
Surya Mohan, P.
546a5b36-7146-4e1a-8db9-041d60f54767
Nair, Prasanth B.
d4d61705-bc97-478e-9e11-bcef6683afe7
Keane, Andy J.
26d7fa33-5415-4910-89d8-fb3620413def
1 March 2008
Surya Mohan, P.
546a5b36-7146-4e1a-8db9-041d60f54767
Nair, Prasanth B.
d4d61705-bc97-478e-9e11-bcef6683afe7
Keane, Andy J.
26d7fa33-5415-4910-89d8-fb3620413def
Surya Mohan, P., Nair, Prasanth B. and Keane, Andy J.
(2008)
Multi-element stochastic reduced basis methods.
Computer Methods in Applied Mechanics and Engineering, 197 (17-18), .
(doi:10.1016/j.cma.2007.11.021).
Abstract
This paper presents mutli-element Stochastic Reduced Basis Methods (ME-SRBMs) for solving linear stochastic partial differential equations. In ME-SRBMs, the domain of definition of the random inputs is decomposed into smaller subdomains or random elements. Stochastic Reduced Basis Methods (SRBMs) are employed in each random element to evaluated the response statistics. These elemental statistics are assimilated to compute the overall statistics. The effectiveness of the method is demonstrated by solving the stochastic steady state heat transfer equation on two geometries involving different types of boundary conditions. Numerical studies are conducted to investigate the h-convergence rates of global and local preconditioning strategies.
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Moha_07.pdf
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Submitted date: 29 November 2006
Published date: 1 March 2008
Keywords:
stochastic reduced basis methods, stochastic partial differential equations, uncertainty quantification, heat transfer, preconditioning
Organisations:
Computational Engineering and Design
Identifiers
Local EPrints ID: 50118
URI: http://eprints.soton.ac.uk/id/eprint/50118
ISSN: 0045-7825
PURE UUID: ea11f790-3207-4c8e-b623-f0f7445bf831
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Date deposited: 28 Jan 2008
Last modified: 16 Mar 2024 02:53
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Author:
P. Surya Mohan
Author:
Prasanth B. Nair
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