Time-harmonic scattering by locally perturbed periodic structures with Dirichlet and Neumann boundary conditions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866913236272545792 |
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| author | Hu, Guanghui Kirsch, Andreas |
| author_facet | Hu, Guanghui Kirsch, Andreas |
| contents | The paper is concerned with well-posedness of TE and TM polarizations of time-harmonic electromagnetic scattering by perfectly conducting periodic surfaces and periodically arrayed obstacles with local perturbations. The classical Rayleigh Expansion radiation condition does not always lead to well-posedness of the Helmholtz equation even in unperturbed periodic structures. We propose two equivalent radiation conditions to characterize the radiating behavior of time-harmonic wave fields incited by a source term in an open waveguide under impenetrable boundary conditions. With these open waveguide radiation conditions, uniqueness and existence of time-harmonic scattering by incoming point source waves, plane waves and surface waves from locally perturbed periodic structures are established under either the Dirichlet or Neumann boundary condition. A DtN operator without using the Green's function is constructed for proving well-posedness of perturbed scattering problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11230 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Time-harmonic scattering by locally perturbed periodic structures with Dirichlet and Neumann boundary conditions Hu, Guanghui Kirsch, Andreas Analysis of PDEs The paper is concerned with well-posedness of TE and TM polarizations of time-harmonic electromagnetic scattering by perfectly conducting periodic surfaces and periodically arrayed obstacles with local perturbations. The classical Rayleigh Expansion radiation condition does not always lead to well-posedness of the Helmholtz equation even in unperturbed periodic structures. We propose two equivalent radiation conditions to characterize the radiating behavior of time-harmonic wave fields incited by a source term in an open waveguide under impenetrable boundary conditions. With these open waveguide radiation conditions, uniqueness and existence of time-harmonic scattering by incoming point source waves, plane waves and surface waves from locally perturbed periodic structures are established under either the Dirichlet or Neumann boundary condition. A DtN operator without using the Green's function is constructed for proving well-posedness of perturbed scattering problems. |
| title | Time-harmonic scattering by locally perturbed periodic structures with Dirichlet and Neumann boundary conditions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.11230 |