Fast, Adaptive, High-Order Accurate Discretization of the Lippmann--Schwinger Equation in Two Dimensions

We present a fast direct solver for two-dimensional scattering problems, where an incident wave impinges on a penetrable medium with compact support. We represent the scattered field using a volume potential whose kernel is the outgoing Green's function for the exterior domain. Inserting this representation into the governing partial differential equation, we obtain an integral equation of Lippmann--Schwinger type. The principal contribution...