Toward the Design of the Global Multi-Trace Volume-Surface Vector-Potential Integral Equations in Inhomogeneous Dielectric Media

The scattering and transmission problem for the vector potential in complex composite structures containing both uniform and non-uniform regions, is tackled in this contribution with a novel volume-surface global multi-trace domain decomposition method. Touching domains are conceptually separated by the global multi-trace method. The vector potential in the inhomogeneous dielectric material domains is expressed in terms of both a pair of surface-supported traces and a volumesupported contrast current, whereas in the homogeneous domains only surface-supported unknowns are required, resulting in fewer degrees of freedom than when using a volume integral representation everywhere. The method is validated within the energy norm.