Efficient Combination of Scalar-Potential Representations of Solenoidal Functions and Quasi-Helmholtz Projectors

Among the most mature approaches to stabilize the electric field integral equation (EFIE) for low frequencies are quasi-Helmholtz projectors. In this work, we show how to adapt these projectors such that the right-hand side can be discretized in a stable manner on multiply-connected geometries, preventing otherwise occurring catastrophic round-off errors. To this end, an approach to combine the quasi-Helmholtz projectors with a scalar-potential representation of solenoidal functions is presented. Furthermore, we provide a strategy to efficiently compute the corresponding projectors via the Schur complement, all of which is corroborated by numerical results.