Fast spectral evaluation of reaction integrals for separated domains

The issue of numerical evaluation of reaction integrals between functions having separated domains arises in several applications of the method of moments (MoM) to the integral-evaluation formulation of electromagnetic problems. Most notably it is important in the context of printed structures life patch antennas or arrays where the two functions may be either entire-domain basis functions on different metallic patches, or subdomain functions on the same patch, or on different patches. Its importance is also clear for in the case of mutual impedances of apertures in arrays (in free space or in a conductor-backed environment). We describe a technique based on the numerical integration along the SDP to efficiently evaluate the spectral reaction integrals between two arbitrary functions on separated domains, in a general stratified dielectric medium. An application example is presented.