A Novel, Symmetrical Solenoidal Basis for the MoM Analysis of Closed Surfaces

In low-frequency, or dense-mesh problems, the electric field integral equation (EFIE) discretization requires the extraction of the solenoidal part of the current to avoid severe bad conditioning of the method of moments (MoM) matrix. The common approach to do this is using the loop basis functions for the solenoidal part. Here we show that the conventional loop basis has poor performances when applied to closed bodies. We identify the reason of this behavior and propose a new solenoidal basis that is free of this problem. In addition, the associated generation algorithm also automatically detects topological complexities (like handles) and produces a basis with significantly improved performances, as confirmed by the reported numerical examples. The basis generation complexity as well as memory requirements-or sparsity-for the proposed basis are O(N log N).