2D compact frequency-domain stencils for dielectric media with an interface

The method of connected local fields, CLF [1,2] is becoming a viable numerical technique for obtaining solutions of the Helmholtz equation in complex media. In CLF the EM fields are expressed as collection of overlapping local fields called patches. In a 2D homogeneous medium we show that the local field in a given FD cell can be approximated by truncated Fourier-Bessel series (FBS) and the FBS coefficients are related to the control points on the surface of the given patch. As part of the effort for extending CLF capability to modeling EM waves in inhomogeneous media, we report in this paper, two numerical techniques for obtaining 2D CLF-based compact frequency-domain stencils for EM fields and waves near a dielectric interface.