A growing number of technologies (communications, imaging, solar energy, etc) rely on manipulating linear waves at the wavelength scale, and accurate numerical modeling is key for device design. I will focus on diffraction problems where time-harmonic scalar waves scatter from piecewise-uniform periodic media. After reviewing the integral equation method, I explain two innovations that allow our solvers to be high-order, robust, and optimal O(N) complexity: 1) new surface quadrature schemes in 2D and 3D compatible with the fast multipole method, and 2) a simple way to "periodize" the integral equation so that the unknowns live on only a single period of the geometry. The resulting linear systems are solved iteratively or in a fast direct fashion. I will present efficient solvers for gratings with up to a thousand periodic interfaces or inclusions. We are extending the techniques to other boundary value problems such as Stokes flow. This is joint work with: Min Hyung Cho, Jun Lai, Adrianna Gillman, Leslie Greengard, Andreas Kloeckner, Mike O'Neil, Zydrunas Gimbutas.
Efficient numerical methods for wave scattering in periodic geometries
Alex Barnett, Dartmouth College & Simons Foundation
Feb 2 2015 - 4:30pm