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arXiv · 2505.23216

Trefftz Discontinuous Galerkin methods for scattering by periodic structures

Armando Maria Monforte·Andrea Moiola
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Abstract

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.

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Armando Maria Monforte, Andrea Moiola. 2025-05-29. Trefftz Discontinuous Galerkin methods for scattering by periodic structures. https://arxiv.org/abs/2505.23216

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