Prof. Xiaobing H. Feng

Department of Mathematics, University of Tennessee, USA

Room 1218, Buidling 3, IAP

14:30, Jan 7, 2020

Abstract

In this talk I shall present a newly developed reduced sampling Monte Carlo approach for wave scattering in random media and for general random PDEs (as well as stochastic PDEs). This approach is based on a multi-modes representation of the solution of the random PDE, as a result, the original random PDE is reduced to a finite number of almost deterministic PDEs with random source terms. Efficient numerical methods and solvers can be formulated for solving the reduced problems.

Random acoustic and elastic Helmholtz equations and random Maxwell equations, which govern respectively acoustic, elastic and electromagnetic wave scattering in random media, will be discussed in detail to explain the main ideas of the proposed approach. Convergence and numerical experiments will be presented to demonstrate the potential advantages of the proposed approach. Extension to random diffusion equations will also be briefly discussed.