Hierarchical bases regularizations of the EFIE without the search for global loops

This work presents a new hierarchical preconditioner for the Electric Field Integral Equation that, differently from all hierarchical preconditioners currently available, applies to both simply- and multiply-connected geometries without the need of recovering the global loops. The new scheme is obtained by leveraging quasi-Helmholtz projectors that allow for an implicit separation of the solenoidal and nonsolenoidal solution part of the current and thus render unnecessary any further explicit determination of the harmonic current (the global loops). Numerical results will corroborate the theoretical developments and will show the impact of our technique on the currently available state-of-the-art.