arXiv subjects

Armando Maria Monforte

Publications and source records attributed to Armando Maria Monforte.

4 recordsLinked to original sources

arXiv2026

Trefftz DG Approximation of the T-Matrix for Scattering by Periodic Layered Structures

We study the scattering of time-harmonic electromagnetic waves by periodic layered gratings, modelled by the 2D Helmholtz equation. The periodic obstacle may include penetrable and impenetrable regions, and consists of a finite number of stacked layers. The boundary value problem is formulated on a single periodic cell using quasi-periodic boundary conditions. The radiation condition in the vertical directions is imposed through Dirichlet-to-Neumann (DtN) operators. To efficiently treat multilayer configurations, we adopt a formulation based on the T-matrix method. The global scattering problem is decomposed into boundary value problems posed on individual layers. On the layer boundaries, the field is expressed in terms of quasi-periodic modal expansions, and the layer T-matrix describes the map between incoming and outgoing wave modes. Each local T-matrix is approximated numerically using a plane-wave based Trefftz Discontinuous Galerkin (TDG) method, which provides an efficient discretization of the layer scattering response. The T-matrix technique leads to linear computational complexity in the number of layers in the grating.

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arXiv2026

TMATDG: applying TDG methods to multiple scattering via T-matrix approximation

We present a MATLAB package for the solution of multiple scattering problems, coupling Trefftz Discontinuos Galerkin methods for Helmholtz scattering with the T-matrix method. We rely on the TMATROM package to numerically approximate the T-matrices and deal with multiple scattering problem, providing a framework to handle scattering by polygonal obstacles.

math.NA↗

arXiv2026

Trefftz Discontinuous Galerkin methods for scattering by periodic structures

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.

math.NA↗

arXiv2023

Plane Wave Discontinuous Galerkin methods for scattering by periodic structures

This thesis explores the application of Plane Wave Discontinuous Galerkin (PWDG) methods for the numerical simulation of electromagnetic scattering by periodic structures. Periodic structures play a pivotal role in various engineering and scientific applications, including antenna design, metamaterial characterization, and photonic crystal analysis. Understanding and accurately predicting the scattering behavior of electromagnetic waves from such structures is crucial in optimizing their performance and advancing technological advancements. The thesis commences with an overview of the theoretical foundations of electromagnetic scattering by periodic structures. This theoretical dissertation serves as the basis for formulating the PWDG method within the context of wave equation. The DtN operator is presented and it is used to derive a suitable boundary condition. The numerical implementation of PWDG methods is discussed in detail, emphasizing key aspects such as basis function selection and boundary conditions. The algorithm's efficiency is assessed through numerical experiments. We then present the DtN-PWDG method, which is discussed in detail and is used to derive numerical solutions of the scattering problem. A comparison with the finite element method (FEM) is presented. In conclusion, this thesis demonstrates that PWDG methods are a powerful tool for simulating electromagnetic scattering by periodic structures.

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