Comparison of integral equations for the Maxwell transmission problem with general permittivities
Journal article, 2021

Two recently derived integral equations for the Maxwell transmission problem are compared through numerical tests on simply connected axially symmetric domains for non-magnetic materials. The winning integral equation turns out to be entirely free from false eigenwavenumbers for any passive materials, also for purely negative permittivity ratios and in the static limit, as well as free from false essential spectrum on non-smooth surfaces. It also appears to be numerically competitive to all other available integral equation reformulations of the Maxwell transmission problem, despite using eight scalar surface densities.

Maxwell’s equations

Electromagnetic scattering

Transmission problem

Non-smooth object

Surface plasmon wave

Boundary integral equation


Johan Helsing

Lund University

Anders Karlsson

Lund University

Andreas Rosén

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Advances in Computational Mathematics

1019-7168 (ISSN) 1572-9044 (eISSN)

Vol. 47 5 76

Subject Categories

Computational Mathematics

Other Physics Topics

Mathematical Analysis



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