An extended charge-current formulation of the electromagnetic transmission problem

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A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all wavenumbers in the closed upper half-plane belonging to argument sets for which Maxwell's equations have unique solutions. This includes the challenging combination of a real positive wavenumber in the outer region and an imaginary wavenumber inside the object. The formulation, or variants thereof, is particularly suitable for numerical field evaluations as confirmed by examples involving both smooth and nonsmooth objects.

Original languageEnglish
Pages (from-to)951-976
Number of pages26
JournalSIAM Journal on Applied Mathematics
Issue number2
Publication statusPublished - 2020 Apr 20

Subject classification (UKÄ)

  • Computational Mathematics


  • Electromagnetic scattering
  • Maxwell's equations
  • Surface plasmon wave
  • Transmission problem


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