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An Efficient and Parallelizable Numerical Method For Random and Stochastic Partial Differential Equations
Source: LASG    Viewed:  time(s)    Time: 2016-7-23
 Prof. Xiaobing H. Feng
Department of Mathematics, University of Tennessee, USA
10:00 am,22 July,2016
No.303,Keyan Building


In this talk I shall present a newly developed multi-modes reduced sampling Monte Carlo numerical approach for solving random and stochastic partial differential equations (PDEs). It is based on the idea of writing the solution of a random PDE into its multi-modes representation. As a result, the original random PDE problem is reduced to a finite number of deterministic problems with random source terms. Efficient and parallelizable numerical methods and algorithms can be easily formulated for solving the reduced problems. The random diffusion equation, which describes flow in random porous media, and the random Helmholtz equation, which governs acoustic wave scattering in random media, will be discussed in detail to explain the idea and concept of the new approach. Convergence analysis and numerical experiments will be presented to demonstrate the potential advantages of the proposed numerical approach.

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