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Integral formulation of Klein-Gordon singular waveguides

Guillaume BalJeremy HoskinsSolomon QuinnManas Rachh
Dec 2022
摘要
We consider the analysis of singular waveguides separating insulating phasesin two-space dimensions. The insulating domains are modeled by a massiveSchr\"odinger equation and the singular waveguide by appropriate jumpconditions along the one-dimensional interface separating the insulators. Wepresent an integral formulation of the problem and analyze its mathematicalproperties. We also implement a fast multipole and sweeping-acceleratediterative algorithm for solving the integral equations, and demonstratenumerically the fast convergence of this method. Several numerical examples ofsolutions and scattering effects illustrate our theory.
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