Integral formulation of Klein-Gordon singular waveguides
Mathematical Physics
2024-08-13 v2 Numerical Analysis
Analysis of PDEs
math.MP
Numerical Analysis
Abstract
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.
Cite
@article{arxiv.2212.12619,
title = {Integral formulation of Klein-Gordon singular waveguides},
author = {Guillaume Bal and Jeremy Hoskins and Solomon Quinn and Manas Rachh},
journal= {arXiv preprint arXiv:2212.12619},
year = {2024}
}