Integral formulation of Klein-Gordon singular waveguides
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866917744986816512 |
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| author | Bal, Guillaume Hoskins, Jeremy Quinn, Solomon Rachh, Manas |
| author_facet | Bal, Guillaume Hoskins, Jeremy Quinn, Solomon Rachh, Manas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_12619 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Integral formulation of Klein-Gordon singular waveguides Bal, Guillaume Hoskins, Jeremy Quinn, Solomon Rachh, Manas Mathematical Physics Numerical Analysis Analysis of PDEs 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. |
| title | Integral formulation of Klein-Gordon singular waveguides |
| topic | Mathematical Physics Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2212.12619 |