Frequency-robust formulations for electromagnetic scattering by perfect conductors via Helmholtz integral operators

Description

In this talk we introduce a novel class of indirect boundary integral equation (BIE) formulations for the solution of electromagnetic scattering problems from smooth perfect electric conductors (PECs) in three-dimensions. These combined-field-type BIE formulations rely exclusively on classical Helmholtz boundary operators, resulting in frequency-robust and provably well-posed Fredholm second-kind BIEs. Specifically, we prove that the proposed formulations are free from spurious resonances, while retaining the simplicity 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 standard 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 high-order Density Interpolation Nyström methods and fast linear algebra solvers, implemented in the open-source Julia package Inti.jl.

Period	18 Jul 2025
Event title	15th International Conference on Spectral and High Order Methods, ICOSAHOM 2025
Event type	Conference
Conference number	15
Location	Montréal, Canada, QuebecShow on map
Degree of Recognition	International