Multi-trace boundary integral formulations with eddy current models

We are interested in boundary integral formulations adapted to the solution of low frequency inductive electromagnetics in the case where the geometry is partitioned in (potentially irregular) subdomains. In the context of electromagnetics in piecewise homogeneous media, the multi-trace formalism (MTF) provides boundary integral formulations for Maxwell's equations posed at the interfaces between different media, with the unknowns associated to one medium a priori decoupled from the unknowns associated to other media. This makes MTF a comfortable paradigm for integral equation based domain decomposition. This formalism is recent and, so far, has been studied only for electromagnetics in time harmonic regime. In this contribution, we adapt the multi-trace approach to the case where the effective permittivity vanishes in certain subdomains. We study the theoretical properties of these new formulations, and discuss its numerical stability.