An efficient reduced sampling Monte Carlo method for wave scattering in random media
Prof. Xiaobing H. Feng
Department of Mathematics,
University of Tennessee, USA
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.
凤小兵：美国田纳西大学（The University of Tennessee）数学终身教授， 数学系副系主任，数学系研究生学部主任； 西北工业大学长江讲座教授。1983年和1985年分别获西安交大计算数学学士和硕士学位，1992年获美国普度大学（Purdue University）应用和计算数学博学位。凤小兵教授长期从事线性，特别是非线性偏微分方程及其数值解法和算法的研究，并取得了一系列国际领先的成果。在“SIAM Review”,“SIAM J Numerical Analysis”, “Mathematics of Computation”,“Numerische Mathematik”等国际一流专业学术期刊上发表论文100余篇。