  We consider the analysis of singular waveguides separating insulating phases
in two-space dimensions. The insulating domains are modeled by a massive
Schr\"odinger equation and the singular waveguide by appropriate jump
conditions along the one-dimensional interface separating the insulators. We
present an integral formulation of the problem and analyze its mathematical
properties. We also implement a fast multipole and sweeping-accelerated
iterative algorithm for solving the integral equations, and demonstrate
numerically the fast convergence of this method. Several numerical examples of
solutions and scattering effects illustrate our theory.
