Fast Evaluation of Layer Potentials using Quadrature by Expansion for Photonics Applications

Thursday, December 15, 2016 - 4:00pm - 5:00pm
Keller 3-180
Andreas Kloeckner (University of Illinois at Urbana-Champaign)
The boundary value and boundary eigenvalue problems resulting from mathematical models of optical devices require high accuracy in their numerical solution, suggesting the use of numerical methods permitting high-order accuracy. So-called boundary integral equation (BIE) methods are particularly appropriate for models involving piecewise constant coefficients that often occur in these applications. The efficient evaluation of Helmholtz layer potentials, the fundamental mathematical objects involved in BIE methods, is thus of critical importance. I will discuss Quadrature by Expansion (QBX), a method for the evaluation of such layer potentials, strategies with which the method can be incorporated into a fast algorithm such as the Fast Multipole Method (FMM), as well as some example applications of the method to key problems in optics and photonics.