Spatial-frequency localized representations for integral equation reflector analysis

Integral equation solution of the scattering from reflector antennas is usually hampered by computational requirements. A major improvement on the computational efficiency can be achieved by using more efficient representations for the induced currents. Entire-domain (sinusoidal) functions were successfully employed to reduce the number of basis functions in the moment-method (MM) solution for axisymmetric reflectors. Similarly, quasi-localized, band-limited functions, introduced by Hermann (1990), have proved useful in the reduction of memory requirements with the additional bonus of providing a faster evaluation of integrals and a reduction in the impedance matrix fill-time. These expansions have a band-limited nature and their efficiency relies on the band-limited nature of the induced currents on smooth surfaces. As the frequency localization usually involves a compromise on the spatial localization, the choice of entire-domain functions or band-limited functions implies a reduced localization and a more extensive overlap than the usual local functions. This fact ultimately leads to a kind of compromise between storage requirements (spatial-frequency localization) and impedance matrix fill-time (spatial localization). An alternative that arises naturally in this context is the use of basis functions optimally localized in the spatial-frequency/spl times/spatial domain (phase-space (r,k) using a physicist language). We study the application of this idea in the context of axisymmetric reflector scattering.