3D compact FD-FD stencils based on spherical Fourier-Bessel series

Numerical methods for obtaining solutions of complex wave field satisfying Helmholtz equation are of great importance. We extend the work of the method of connected local fields (CLF) to the 3-D case. Using a local field expansion from a truncated spherical Fourier-Bessel series (SFBS) we are able to obtain four variations of 3D compact frequency-domain (FD) stencils. We verify the effectiveness of these 3D compact stencils by computing the numerical 3D Green's function. The results compare well with the analytic solution at a low three points per wavelength sampling density for the most accurate formulation.