Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2505.20440

Maxwell à la Helmholtz: Electromagnetic scattering by 3D perfect electric conductors via Helmholtz integral operators

Juan Burbano-Gallegos·Carlos Pérez-Arancibia·Catalin Turc
View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper introduces a novel class of indirect boundary integral equation (BIE) formulations for the solution of electromagnetic scattering problems involving smooth perfectly electric conductors (PECs) in three-dimensions. These combined-field-type BIE formulations rely exclusively on classical Helmholtz boundary operators, resulting in provably well-posed, frequency-robust, Fredholm second-kind BIEs. Notably, we prove that the proposed formulations are free from spurious resonances, while retaining the versatility of Helmholtz integral operators. The approach is based on the equivalence between the Maxwell PEC scattering problem and two independent vector Helmholtz boundary value problems for the electric and magnetic fields, with boundary conditions defined in terms of the Dirichlet and Neumann traces of the corresponding vector Helmholtz solutions. While certain aspects of this equivalence (for the electric field) have been previously exploited in the so-called field-only BIE formulations, we here rigorously establish and generalize the equivalence between Maxwell and Helmholtz problems for both fields. Finally, a variety of numerical examples highlights the robustness and accuracy of the proposed approach when combined with Density Interpolation-based Nyström methods and fast linear algebra solvers, implemented in the open-source Julia package Inti$.$jl.

Explore related subjects

math.NAcs.NAphysics.comp-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Juan Burbano-Gallegos, Carlos Pérez-Arancibia, Catalin Turc. 2025-05-28. Maxwell à la Helmholtz: Electromagnetic scattering by 3D perfect electric conductors via Helmholtz integral operators. https://arxiv.org/abs/2505.20440

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Fully spectral scheme for the linear BGK equation on the whole space

In this article, we design a fully spectral method in both space and velocity for a linear inhomogeneous kinetic equation with mass, momentum and energy conservation. We focus on the linear BGK equation with a confinement potential $Φ$, even if the method could be applied to different collision operators. It is based upon the projection on Hermite polynomials in velocity and orthonormal polynomials with respect to the weight $e^{-$Φ$}$ in space. The potential $Φ$ is assumed to be a polynomial. It is, to the author's knowledge, the first scheme which preserves hypocoercive behavior in addition to the conservation laws. These different properties are illustrated numerically on both quadratic and double well potential.

math.NA↗
arXiv2026

Inverse inequalities for kernel-based approximation on bounded domains and Riemannian manifolds

This paper establishes inverse inequalities for kernel-based approximation spaces defined on bounded Lipschitz domains in $\mathbb{R}^d$ and compact Riemannian manifolds. While inverse inequalities are well-studied for polynomial spaces, their extension to kernel-based trial spaces poses significant challenges. For bounded Lipschitz domains, we extend prior Bernstein inequalities, which only apply to a limited range of Sobolev orders, to the full range of lower and upper orders, and derive Nikolskii inequalities that bound $L_\infty$ norms by $L_2$ norms. For compact Riemannian manifolds, we focus on restricted kernels, which are defined as the restriction of positive definite kernels from the ambient Euclidean space to the manifold, and prove their counterparts.

math.NA↗
arXiv2026

Error Estimates for Hyperbolic Scaling Limits of Linear Kinetic Models on Networks

This paper studies linear discrete kinetic models on networks and their asymptotic behavior in the small Knudsen number limit. For coupling conditions at an n-edge junction under a symmetric formulation, we introduce a change of variables that reformulates the system into n independent initial-boundary value problems. The asymptotic expansions are then constructed and rigorously justified by deriving an error estimate based on the energy method.

math.NA↗