In this talk, we will present our recent development and analysis of some numerical methods proposed for solving the time-dependent Maxwell's equations with random coefficients and subject to random initial conditions. We provide a rigorous regularity analysis of the solution with respect to the random variables. Stochastic collocation method and generalized polynomial chaos (gPC) approach and their theoretical analysis will be discussed. Finally, numerical results confirming the theoretical analysis will be presented.

Prof. Li Jichun earned his B.S. in Computational Mathematics from Nanjing University and Ph.D. in Applied Mathematics from Florida State University. He worked 2 years (1998-2000) at ICES of University of Texas at Austin before he moved to UNLV in 2000. He was summer faculty researcher at U.S. Air Force Research Laboratory from 2003-2006. During August 2008 - July 2009, Prof. Li served as Associate Director for the Institute for Pure and Applied Mathematics (IPAM) at UCLA. Since July 2010, he has been a Full Professor of Mathematics at UNLV. Prof. Li is very interested in multidisciplinary research related to numerical analysis and scientific computing. His major research areas are on numerical methods (mainly FEM) for PDEs from different disciplinaries. Work include singularly perturbed problems, surface and groundwater modeling, parallel computing with MPI and C++, image processing, radial basis meshless methods, inverse problems, high-order compact difference schemes, Maxwell's equations in metamaterials.