Towards Accurate Discretization of Arbitrary Right-Hand Side Excitations on Multiply-Connected Geometries

For the computation of the field scattered by an object, integral equation formulations such as the electric field integral equation (EFIE), the magnetic field integral equation (MFIE), and the combined field integral equation (CFIE) are well-established techniques. They are flexible, accurate, and computationally efficient. They suffer, however, from different issues when the frequency becomes low: The EFIE and the CFIE become ill-conditioned. Furthermore, for the MFIE significant round-off errors prevent an accurate solution. As a remedy, a quasi¬Helmholtz decomposition of the surface current density into a loop-star or a loop-tree basis can be leveraged [1]. Even more suitable are quasi-Helmholtz projectors derived from the loop-star basis [2]. They avoid the introduction of a dense-discretization breakdown such that in combination with Calderon preconditioning a stable system matrix is obtained.