Comparison of integral equations for the Maxwell transmission problem with general permittivities

Abstract

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.

An efficient full-wave solver for eddy currents

“…See also Section 4 for the notions of dense-mesh breakdown and topological lowfrequency breakdown.) This corresponds to the false eigenwavenumber at 𝑥 = −1 in [17,Fig. 9(b)], and it should be noted that this single peak contains the whole eddy current regime shown in Fig.…”

“…We point out that although arg(𝑘 − ) = 0 and arg(𝑘 + ) = 𝜋∕4 in all our numerical examples, there is no approximation of the full MTP ( 7) involved, and a known permittivity can be included in 𝑘 + . The Dirac BIE from [18,17] is the starting point for the present work and from now on referred to as Dirac (A). This BIE is based on the embedding of Maxwell's equations into an elliptic Dirac equation and a Cauchy integral representation for the fields (Eq.…”

“…It has 12 free parameters, as recalled in (24) below, and these can be chosen to avoid false eigenwavenumbers for all passive materials. As for low-frequency breakdown, the only regimes found in [18,17] where the Dirac (A) exhibits false eigenwavenumbers is when 𝑘 ± → 0 at the same time as k = 𝑘 + ∕𝑘 − → ∞ or k → 0. (We refer to [17,Sec.…”

“…As for low-frequency breakdown, the only regimes found in [18,17] where the Dirac (A) exhibits false eigenwavenumbers is when 𝑘 ± → 0 at the same time as k = 𝑘 + ∕𝑘 − → ∞ or k → 0. (We refer to [17,Sec. 3] for a discussion about the notions of eigenwavenumbers and low-frequency breakdown.…”

Direct Computation of the PEC Body of Revolution Modal Green Function for the Electric Field Integral Equation

“…When the shape of the PEC scatterer exhibits spatial symmetry, the computational costs in evaluating the scattering can sometimes be significantly reduced. This is particularly the case for rotationally symmetric objects, called bodies of revolution (BORs) [3]- [6]. The scattering by PEC BORs has been studied since the 1960s [7]- [10].…”