Solving the low-frequency breakdown of the wire-EFIE without the search for global loops

This work focuses on a strategy for the elimination of the low-frequency breakdown of the wire Electric Field Integral Equation (EFIE) based on the quasi-Helmoltz projectors. Differently from classical quasi-Helmoltz decompositions, the scheme proposed here does not introduce an additional mesh-refinement-related ill conditioning and it does not require the detection of global loops. A special attention will be devoted to the development of ad-hoc linear-in-complexity algorithms to compute the quasi-Helmoltz projectors, which will take full advantage of special tree-like and quasi-tree-like topologies often appearing in wire-EFIE problems. Numerical results will corroborate the theoretical developments and show the practical effectiveness of all newly-presented schemes.