Method of connected local fields for obtaining semi-analytical solutions of the Helmholtz equation

The well-known finite-difference frequency-domain method for the Helmholtz equation requires high spatial sampling density to produce accurate solutions due to numerical grid dispersion. We present the method of connected local field which has a FD-like formulation that connects square patches of overlapping EM fields. Each local field is represented by a truncated Fourier-Bessel series satisfying the Helmholtz equation. We show that the method of connected local fields is a viable, highly-accurate numerical electromagnetic field wave solver.