Inexact Picard iterative scheme for steady-state nonlinear diffusion in random heterogeneous media
Inexact Picard iterative scheme for steady-state nonlinear diffusion in random heterogeneous media
In this paper, we present a numerical scheme for the analysis of steady-state nonlinear diffusion in random heterogeneous media. The key idea is to iteratively solve the nonlinear stochastic governing equations via an inexact Picard iteration scheme, wherein the nonlinear constitutive law is linearized using the current guess of the solution. The linearized stochastic governing equations are then spatially discretized and approximately solved using stochastic reduced basis projection schemes. The approximation to the solution process thus obtained is used as the guess for the next iteration. This iterative procedure is repeated until an appropriate convergence criterion is met. Detailed numerical studies are presented for diffusion in a square domain for varying degrees of nonlinearity. The numerical results are compared against benchmark Monte Carlo simulations, and it is shown that the proposed approach provides good approximations for the response statistics at modest computational effort
046706-[9pp]
Mohan, P. Surya
0622f14f-3ee9-457b-9153-c0fdfbb1dc91
Nair, Prasanth B.
d4d61705-bc97-478e-9e11-bcef6683afe7
Keane, Andy J.
26d7fa33-5415-4910-89d8-fb3620413def
2009
Mohan, P. Surya
0622f14f-3ee9-457b-9153-c0fdfbb1dc91
Nair, Prasanth B.
d4d61705-bc97-478e-9e11-bcef6683afe7
Keane, Andy J.
26d7fa33-5415-4910-89d8-fb3620413def
Mohan, P. Surya, Nair, Prasanth B. and Keane, Andy J.
(2009)
Inexact Picard iterative scheme for steady-state nonlinear diffusion in random heterogeneous media.
Physical Review E, 79 (4), .
(doi:10.1103/PhysRevE.79.046706).
Abstract
In this paper, we present a numerical scheme for the analysis of steady-state nonlinear diffusion in random heterogeneous media. The key idea is to iteratively solve the nonlinear stochastic governing equations via an inexact Picard iteration scheme, wherein the nonlinear constitutive law is linearized using the current guess of the solution. The linearized stochastic governing equations are then spatially discretized and approximately solved using stochastic reduced basis projection schemes. The approximation to the solution process thus obtained is used as the guess for the next iteration. This iterative procedure is repeated until an appropriate convergence criterion is met. Detailed numerical studies are presented for diffusion in a square domain for varying degrees of nonlinearity. The numerical results are compared against benchmark Monte Carlo simulations, and it is shown that the proposed approach provides good approximations for the response statistics at modest computational effort
Text
sury_09.pdf
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Published date: 2009
Organisations:
Computational Engineering and Design
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Local EPrints ID: 71585
URI: http://eprints.soton.ac.uk/id/eprint/71585
ISSN: 1063-651X
PURE UUID: 7f314e56-0645-4e1e-b912-a205c66f91fb
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Date deposited: 15 Dec 2009
Last modified: 14 Mar 2024 02:39
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Author:
P. Surya Mohan
Author:
Prasanth B. Nair
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