A loop-tree basis for metallic surfaces connected to wires

This paper demonstrates an automatic, low-complexity scheme to extract the loop and tree bases from the mesh of complex wire-surface structures, either free-standing or connected to an infinite ground plane. The algorithm is based on graph theory, and is able to handle completely arbitrary wire-surface structures without a priori information on its topological complexity. The presented approach is directly applicable to existing codes that utilize the junction basis previously proposed. To check the performance of the proposed basis, a planar inverted-F antenna is analyzed, in order to demonstrate the numerical behavior of the proposed loop-tree basis.