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Solving Spdes By A Least Squares Method
Manouzi, Hassan;
Manouzi, Hassan;
Solving Spdes By A Least Squares Method
We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itˆo chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. To obtain the chaos coefficients in the corresponding deterministic equations, we use a least square formulation. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.
- Université Laval Canada
- Laval Universitry Canada
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[3] H. Holden, T. Lindstrøm, B. Øksendal, J. Ubøe, and T.-S. Zhang, The pressure equation for fluid flow in a stochastic medium, Potential Analysis, 4 (1995) 655-674.
[4] H. Holden, B. Øksendal, J. Ubøe, and T.-S. Zhang, Stochastic Partial Differential Equations. A Modeling, White Noise Functional Approach, Probability and its Applications. Birkha¨user, Boston, 1996.
[5] M. Kardar, Y.C. Zhang, Scaling of Directed Polymers in Random Media, Physical Review Letters, 58 (1987) 2087-2090.
[6] H. Manouzi, A finite element approximation of linear stochastic PDE's equations driven by a multiplicative white noise, International Journal of Computer Mathematics, 85 (2008) 527-546. [OpenAIRE]
[7] T. G. Theting, Solving Wick-stochastic boundary value problems using a finite element method, Stochastics Stochastics Rep. 70 (200) 241-270.
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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
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This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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- Université Laval Canada
- Laval Universitry Canada
We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itˆo chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. To obtain the chaos coefficients in the corresponding deterministic equations, we use a least square formulation. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.