In the context of hybrid formulations, the Poincaré-Steklov operator acting on traces of solutions to the vector Helmholtz equation in a heterogeneous interior domain with a smooth boundary is regularized by a well-known boundary integral operator related to the homogeneous exterior domain. For the first time, this property allows us to simultaneously construct a Calderón multiplicative preconditioner for the discretized operator and for a 3-D hybrid finite/boundary element method formulation, applicable to electromagnetic scattering problems. Numerical examples demonstrate the effectiveness of this novel preconditioning scheme, even for heterogeneous domains with non-smooth boundaries.

Abstract-In this paper, some properties of dispersion curves in general isotropic piecewise homogeneous waveguides are rigorously derived. These properties are leveraged in a numerical implementation capable of determining the dispersion curves of such waveguides with cross-section materials that can be highly conductive (such as copper). In a numerical example, the influence of a lossy shielding conductor on the complex modes of a shielded dielectric image guide is investigated for the first time.

The solution of the time-harmonic Maxwell equations using a boundary element method, for 2-D geometries illuminated by arbitrary 3-D excitations, gives rise to numerical difficulties if highly conductive media are present. In particular, the interaction integrals arising in the method of moments involve kernels that strongly oscillate in space and, at the same time, decay exponentially. We present an accurate method to tackle these issues over a very broad conductivity range (from lossy dielectric to conductor skin-effect regime), for both magnetic and nonmagnetic conductors. Important applications are the modal analysis of waveguides with nonperfect conductors, scattering problems, and shielding problems with enclosures with arbitrary permeability and conductivity and 3-D noise sources.

Abstract-Recent developments in high-speed interconnects show a clear tendency towards higher bitrates, emphasizing the need for a reliable prediction of the waveguide behavior. We present a frequency domain eigenmode analysis of isotropic waveguides using a boundary element method. Some properties of the dispersion curves can be beneficially leveraged into the numerical framework for calculating the waveguide characteristics as a function of frequency. The method allows the incorporation of highly conductive materials, which is demonstrated in a numerical example.