Trefftz Discontinuous Galerkin methods for scattering by periodic structures
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912880075472896 |
|---|---|
| author | Monforte, Armando Maria Moiola, Andrea |
| author_facet | Monforte, Armando Maria Moiola, Andrea |
| contents | We propose a Trefftz discontinuous Galerkin (TDG) method for the approximation of plane wave scattering by periodic diffraction gratings, modelled by the two-dimensional Helmholtz equation. The periodic obstacle may include penetrable and impenetrable regions. The TDG method requires the approximation of the Dirichlet-to-Neumann (DtN) operator on the periodic cell faces, and relies on plane wave discrete spaces. For polygonal meshes, all linear-system entries can be computed analytically. Using a Rellich identity, we prove a new explicit stability estimate for the Helmholtz solution, which is robust in the small material jump limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23216 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Trefftz Discontinuous Galerkin methods for scattering by periodic structures Monforte, Armando Maria Moiola, Andrea Numerical Analysis We propose a Trefftz discontinuous Galerkin (TDG) method for the approximation of plane wave scattering by periodic diffraction gratings, modelled by the two-dimensional Helmholtz equation. The periodic obstacle may include penetrable and impenetrable regions. The TDG method requires the approximation of the Dirichlet-to-Neumann (DtN) operator on the periodic cell faces, and relies on plane wave discrete spaces. For polygonal meshes, all linear-system entries can be computed analytically. Using a Rellich identity, we prove a new explicit stability estimate for the Helmholtz solution, which is robust in the small material jump limit. |
| title | Trefftz Discontinuous Galerkin methods for scattering by periodic structures |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2505.23216 |