During the last two decades, fast algorithms have brought a variety of large-scale physical and biophysical modeling tasks within practical reach. This is particularly true of integral equation approaches to electromagnetics, acoustics, gravitation, elasticity, and fluid dynamics. The practical application of these methods, however, requires analytic representations that lead to well-conditioned linear systems, quadrature methods that permit the accurate evaluation of boundary integrals with singular kernels, and techniques for a posteriori error estimation that permit robust mesh refinement. At the 2014 SIAM Annual Meeting Leslie Greengard of the Simons Foundation and Courant Institute of Mathematical Sciences, New York University, gave an overview of recent progress in these areas with a particular emphasis on wave scattering problems in complex geometry via The John von Neumann Lecture. View the video for an overview of his talk:
View the full presentation.