Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2
Search results for: SPDEs
2 Solving SPDEs by Least Squares Method
Authors: Hassan Manouzi
Abstract:
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.Keywords: least squares, wick product, SPDEs, finite element, wiener chaos expansion, gradient method
Procedia PDF Downloads 4131 Solving Stochastic Eigenvalue Problem of Wick Type
Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati
Abstract:
In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Ito chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.Keywords: eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Ito chaos expansion
Procedia PDF Downloads 352