In order to accurately compute scattered and radiated fields in the presence of arbitrary excitations, a low-frequency stable discretization of the right-hand side (RHS) of a quasi-Helmholtz preconditioned electric field integral equation (EFIE) on multiply-connected geometries is introduced, which avoids an ad-hoc extraction of the static contribution of the RHS when tested with solenoidal functions. To obtain an excitation agnostic approach, our approach generalizes a technique to multiply-connected geometries where the testing of the RHS with loop functions is replaced by a testing of the normal component of the magnetic field with a scalar function. To this end, we leverage orientable global loop functions that are formed by a chain of Rao-Wilton-Glisson (RWG) functions around the holes and handles of the geometry, for which we introduce cap surfaces that allow to uniquely define a suitable scalar function. We show that this approach works with open and closed, orientable and non-orientable geometries. The numerical results demonstrate the effectiveness of this approach.

In order to low-frequency stabilize the electric field integral equation (EFIE) when discretized with divergence conforming B-spline based basis and testing functions in an isogeometric approach, we propose a corresponding quasi-Helmholtz preconditioner. To this end, we derive i) a loop-star decomposition for the B-spline basis in the form of sparse mapping matrices applicable to arbitrary polynomial orders of the basis as well as to open and closed geometries described by single-or multipatch parametric surfaces (as an example non-uniform rational Bsplines (NURBS) surfaces are considered). Based on the loopstar analysis, we show ii) that quasi-Helmholtz projectors can be defined efficiently. This renders the proposed low-frequency stabilization directly applicable to multiply-connected geometries without the need to search for global loops and results in betterconditioned system matrices compared to directly using the loopstar basis. Numerical results demonstrate the effectiveness of the proposed approach.

In order to accurately compute scattered and radiated fields in the presence of arbitrary excitations, a lowfrequency stable discretization of the right-hand side (RHS) of a quasi-Helmholtz preconditioned electric field integral equation (EFIE) on multiply-connected geometries is introduced, which avoids an ad-hoc extraction of the static contribution of the RHS when tested with solenoidal functions. To obtain an excitation agnostic approach, our approach generalizes a technique to multiply-connected geometries where the testing of the RHS with loop functions is replaced by a testing of the normal component of the magnetic field with a scalar function. To this end, we leverage orientable global loop functions that are formed by a chain of Rao-Wilton-Glisson (RWG) functions around the holes and handles of the geometry, for which we introduce cap surfaces that allow to uniquely define a suitable scalar function. We show that this approach works with open and closed, orientable and non-orientable geometries. The numerical results demonstrate the effectiveness of this approach.

The accurate solution of quasi-Helmholtz decomposed electric field integral equations (EFIEs) in the presence of arbitrary excitations is addressed: Depending on the specific excitation, the quasi-Helmholtz components of the induced current density do not have the same asymptotic scaling in frequency, and thus, the current components are solved for with, in general, different relative accuracies. In order to ensure the same asymptotic scaling, we propose a frequency normalization scheme of quasi-Helmholtz decomposed EFIEs which adapts itself to the excitation and which is valid irrespective of the specific excitation and irrespective of the underlying topology of the structure. Specifically, neither an ad-hoc adaption nor a-priori information about the excitation is needed as the scaling factors are derived based on the norms of the right-hand side (RHS) components and the frequency. Numerical results corroborate the presented theory and show the effectiveness of our approach.