Speaker: Mike O’Neil, NYU

 

Title: Advances in fast high-order boundary integral equation solvers in complex geometries in three dimensions

 

Abstract: The fast multipole method (FMM) was invented over 30 years ago and has enabled the asymptotically optimal solution of dense linear systems arising from the discretization of integral equations appearing in acoustics, electromagnetics, fluid flow, etc. However, in order to build FMM-accelerated high-order solvers in three dimensions, additional advances in mesh generation and quadrature are also required; efficient coupling of these schemes to the FMM itself is also of importance.

In this talk I will give an overview of the ingredients needed to build boundary integral equation solvers in three dimensions, and then detail some recent advances in high-order mesh generation and quadrature. Numerical examples for the Helmholtz and Laplace-Beltrami equations will be shown.