Section: New Results

Quasi-local Multi-Trace formulations for electromagnetics

Multi-trace formulations (MTF) are a general methodology to derive first kind boundary integral formulations for harmonic wave scattering problems posed in multi-domain geometrical confgurations. There exists both a local and a global variant of MTF that only differ through the way transmission conditions are imposed across interfaces. Global MTF is easier to analyse but, from a computational viewpoint, local MTF appears more appealing because it looks computationally cheaper.

As regards local MTF, a decent stability theory has been developped for acoustic scalar wave propagation, but no such result as Garding inequality or uniform discrete inf-sup condition has been established so far for local MTF in the case of electromagnetics. Wether or not local MTF is stable for electromagnetics is actually an open question presently.

In this work, we have adopted a slightly modified version of local MTF where tranmission conditions are imposed by means of an operator that is non-local, but with a kernel whose support can be as small as desired. This so-called quasi-local MTF approach has previsouly been developped for acoustics and we adapted it to the case of electromagnetics. We could in particular prove a Garding inequality for quasi-local MTF applied to electromagnetics, and thus obtain uniform discrete inf-sup condition.