Monday, Nov 12, 11:30AM-12:30 PM, Fretwell 315

November 08, 2018 by Duan Chen
Categories: Spring 2022
Dr. Min Hyung Cho,  University of Massachusetts at Lowell 
Title: Fast Integral equation methods for wave scattering in layered media
Abstract: Many modern electronic/optical devices rely on waves such as solar cells, antennae, radar, and lasers. These devices are mostly built on a patterned layered structure. For optimizing and characterizing these devices, numerical simulations play a crucial role. In this talk, an integral equation method in 2- and 3-D layered media Helmholtz equation will be presented. In 2-D, the boundary integral equation with the periodizing scheme is used. This method uses near- and far-field decomposition to avoid using the quasi-periodic Green’s function. By construction, the far-field contribution can be compressed using Schur complement with minimal computational cost. The new method solved the scattering from a 1000-layer with 300,000 unknown to 9-digit accuracy in 2.5 minutes on a workstation. In 3-D, a Lippmann-Schwinger type volume integral equation is used with layered media Green’s function to include interface condition between layers and reduces the problem to only scatterers.

In both 2- and 3-D layered media, a fast integral operator application is required because integral equation methods usually yield a dense matrix system. A heterogenous fast multipole method (H-FMM) is developed. This is a hierarchical method and uses recursively-generated tree-structure. The interactions from far fields are compressed with free-space multipole expansion. All the spatially variant information are collected into the multipole-to-local translation operators. As a result, many free-space tools can be adapted directly without any modification to obtain an optimal O(N) algorithm for low frequency.
This is a joint work with Jingfang Huang (UNC), Alex Barnett (Dartmouth College), Duan Chen (UNC Charlotte), and Wei Cai (Southern Methodist University)