2022/12/23 by Guillaume Bal, Bal, Guillaume, Jeremy Hoskins +5 · 2 citations
Engineering · Physics and Astronomy · Mathematics · #Electromagnetic Simulation and Numerical Methods #Electromagnetic Scattering and Analysis #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2212.12619
We consider the analysis of singular waveguides separating insulating phases in two-space dimensions. The insulating domains are modeled by a massive Schrödinger 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.