Integral equation based fast solvers for periodic scattering problems

Tuesday, December 13, 2016 - 9:00am - 10:00am
Keller 3-180
Alex Barnett (Dartmouth College)
Integral equations can enable the efficient and accurate solution of wave diffraction problems from piecewise uniform media. However, the usual quasiperiodic Green's function approach has certain disadvantages, including non-robustness. I will explain a spectrally-accurate alternative that combines free-space Green's kernels with a set of auxiliary particular solutions, whose coefficients are solved in the least squares sense. I will show how it is useful for various challenging Helmholtz and Maxwell problems in 2D and 3D.

Joint work with: Min Hyung Cho, Yuxiang Liu, Adrianna Gillman, Jun Lai, Motoki Kobayashi, and Leslie Greengard.