Carlos Perez-Arancibia: Maxwell à la Helmholtz: Helmholtz Boundary Integral Equations for Electromagnetic Scattering

Speaker
Carlos Perez-Arancibia, University of Twente

Abstract
We present a new class of indirect boundary integral equation (BIE) formulations for solving electromagnetic scattering problems involving smooth perfectly electric conducting (PEC) obstacles in three dimensions. These combined-field-type formulations are constructed entirely from classical scalar Helmholtz boundary operators applied componentwise, leading to Fredholm second-kind integral equations that are provably well-posed and stable across all frequencies. The formulations are based on a classical acoustic combined field ansatz, extended to vector fields by acting on each component. This structure ensures the absence of spurious resonances while preserving the simplicity of Helmholtz BIEs. The key idea is an equivalence between the Maxwell PEC scattering problem and two decoupled vector Helmholtz boundary value problems—one for the electric field and one for the magnetic field—with boundary conditions expressed through their Dirichlet and Neumann traces. Numerical experiments, implemented in the open-source Julia package Inti.jl, showcase the accuracy and robustness of the methodology, which relies on Density Interpolation-based Nyström discretizations and fast iterative linear algebra solvers based on GMRES, FMM, and H-matrix techniques.