Applied Math Seminar: Stochastic Algorithms for Electromagnetic Problems of Nano-Structures

Seminar | April 25 | 11 a.m.-12 p.m. | 891 Evans Hall

 Wei Cai, Southern Methodist University

 Department of Mathematics

In this talk, we will present some stochastic algorithms and numerical results for solving electromagnetic problems in nano-particles and random meta-materials. Firstly, we will present a path integral Monte Carlo method for computing magnetic polarizability tensors of nano-particles of complex geometries for material sciences applications. The method relies on a Feynman-Kac formula involving reflecting Brown motions (RBMs) and accurate computation of the local time of the RBMs using a random walk-on-spheres technique. Secondly, in order to optimize functional properties of 3-D random meta-materials (MMs), we will present a stochastic representation scheme for random MMs with volume exclusion constrains and given correlations, a fast volume integral equation electromagnetic solver for the scattering of a large number of meta-atoms of typical geometric shapes (cubes, spheres, and ellipses) in layered media, and a procedure to optimize the optical properties of the MMs. A new fast multipole method for 3-D Helmholtz equation for layered media will be presented based on new multipole expansion (ME) and multipole to local translation (M2L) operators for layered media Green's functions.